Skip to main content
SpringerLink
Log in

Progress in free associative algebras

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • S. A. Amitsur 57,A generalization of Hilbert’s Nullstellensatz, Proc. Amer. Math. Soc.8 (1957), 649–656.

    Article  MATH  MathSciNet  Google Scholar 

  • S. A. Amitsur 66,Rational identities and applications to algebra and geometry, J. Algebra3 (1966), 304–359.

    Article  MATH  MathSciNet  Google Scholar 

  • M. A. Arbib 69,Theories of Abstract Automata, Englewood Cliffs, N. J., 1969.

  • G. M. Bergman 67,Commuting elements in free algebras and related topics in ring theory; Thesis, Harvard University, 1967.

  • G. M. Bergman 69,Centralizers in free associative algebras, Trans. Amer. Math. Soc.137 (1969), 327–344.

    Article  MATH  MathSciNet  Google Scholar 

  • G. M. Bergman 70,Skew fields of non-commutative rational functions, after Amitsur, Sém. Schützenberger-Lentin-Nivat, Année 1969/70, Paris, 1970.

  • G. M. Bergman 74a,The diamond lemma for ring theory, to appear.

  • G. M. Bergman 74b,Modules over coproducts of rings, Trans Amer. Math. Soc.

  • G. M. Bergmana,Notes on epimorphisms of rings, unpublished.

  • G. M. Bergman and W. Dicks, 74,Universal derivations, J. Algebra.

  • N. Bourbaki 50,Algèbre, Ch. IV, Paris, 1950.

  • A. Brumer 66,Pseudocompact algebras, profinite groups and class formations, J. Algebra4 (1966), 442–470.

    Article  MATH  MathSciNet  Google Scholar 

  • N. Chomsky and M. P. Schützenberger 63,The algebraic theory of context-free languages, Computer Programming and Formal Systems, P. Braffort and D. Hirschberg (eds.) Amsterdam, 1963.

  • W. E. Clark and G. M. Bergman 73,The automorphism class group of the category of rings, J. Algebra24 (1973), 80–99.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 54a,On homomorphic images of special Jordan algebras, Canad. J. Math.6 (1954), 253–264.

    MATH  Google Scholar 

  • P. M. Cohn 54b,Sur le critère de Friedrichs pour les commutateurs dans une algèbre associative libre, C. R. Acad. Sci. (Paris)239 (1954), 743–745.

    MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 59,On the free product of associative rings, Math. Z.71 (1959), 380–398.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 60,On the free product of associative rings II. The case of (skew) fields, Math. Z.73 (1960), 433–456.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 61a,On a generalization of the Euclidean algorithm, Proc. Cambridge Phil. Soc.57 (1961), 18–30.

    MATH  Google Scholar 

  • P. M. Cohn 61b,On the embedding of rings in skew fields, Proc. London Math. Soc. (3)11 (1961), 511–530.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 61c,Quadratic extensions of skew fields, Proc. London Math. Soc. (3)11 (1961), 531–556.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 62a,Free Rings, Lecture Notes, Yale University, 1962.

  • P. M. Cohn 62b,Factorization in non-commutative power series rings, Proc. Cambridge Phil. Soc.58 (1962), 452–464.

    MATH  Google Scholar 

  • P. M. Cohn 63a,Non-commutative unique factorization domains, Trans. Amer. Math. Soc.109 (1963), 313–331.

    Article  MathSciNet  Google Scholar 

  • P. M. Cohn 63b,Rings with a weak algorithm, Trans. Amer. Math. Soc.109 (1963), 332–356.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 64a,Subalgebras of free associative algebras, Proc. London Math. Soc. (3)14 (1964), 618–632.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 64b,Free ideal rings, J. Algebra1 (1964), 47–69.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 65,Universal Algebra, New York, London, Tokyo, 1965.

  • P. M. Cohn 66,On a class of binomial extensions, Illinois J. Math.10 (1966), 418–424.

    MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 69a,Free associative algebras, Bull. London Math. Soc.1 (1969), 1–39.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 69b,Dependence in rings II. The dependence number, Trans. Amer. Math. Soc.135 (1969), 267–279.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 70a,Progrès récent dans l’étude des algèbres associatives libres, Sém. Dubreil-Pisot, 22e année, 1968/69, Paris, 1970.

  • P. M. Cohn 70b,On a class of rings with inverse weak algorithm, Math. Z.117 (1970), 1–6.

    Article  MathSciNet  Google Scholar 

  • P. M. Cohn 71a,The embedding of firs in skew fields, Proc. London Math. Soc. (3)23 (1971), 193–213.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 71b,Free Rings and their Relations, London and New York, 1971.

  • P. M. Cohn 71c,Free ideal rings and free products of rings, Actes, Congrès Internat. Math. 1970, Tome 1, 1971, pp. 273–278.

  • P. M. Cohn 71d,The embedding of radical rings in simple radical rings, Bull. London Math. Soc.3 (1971), 185–188.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 72a,Skew fields of fractions and the prime spectrum of a general ring, Lecture Notes on Rings and Modules, Springer Lecture Notes No. 246, Berlin, 1972.

  • P. M. Cohn 72b,Rings of fractions, Lecture Notes, University of Alberta, 1972.

  • P. M. Cohn 72c,K 2 of polynomial rings and free algebras, Ring Theory, R. Gordon (ed.), Proc. of conference on ring theory held at Park City, Utah. New York, 1972.

  • P. M. Cohn 73a,Unique factorization domains. Amer. Math. Monthly80 (1973), 1–17.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 73b,Free radical rings, Colloq. Math. Soc.1. Bolyai, Vol.6, Rings, Modules and Radicals, Keszthely, (Hungary). Groningen, 1973, pp. 135–145.

  • P. M. Cohn, 73c,The word problem for free fields, J. Symbolic Logic38 (1973), 309–314.correction and addendun ibid. 40 (1975) (in press).

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 73d,Free products of skew fields, J. Austral. Math. Soc.16 (1973), 300–308.

    MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 73e,Inversive localization in Noetherian rings, Comm. Pure App. Math.27 (1973), 679–691.

    Article  Google Scholar 

  • P. M. Cohn 74a,Localization in semifirs, Bull. London Math. Soc.6 (1974), 13–20.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 74b,The class of rings embeddable in skew fields, Bull. London Math. Soc.6 (1974), 147–148.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Cohn 75a,Presentations of skew fields I. Existentially closed skew fields and the Nullstellensatz, Math. Proc. Camb. Phil. Soc.77 (1975), (in press).

  • P. M. Cohn 75b,Algebra and Language theory Bull. London Math. Soc.7 (1975) (in press).

  • P. M. Cohna,The affine scheme of a general ring (unpublished).

  • J. H. Cozzens 72,Simple principal left ideal domains, J. Algebra23 (1972), 66–75.

    Article  MATH  MathSciNet  Google Scholar 

  • A. J. Czerniakiewicz 71,Automorphisms of a free associative algebra of rank 2, I, Trans. Amer. Math. Soc.160 (1971), 393–401.

    Article  MATH  MathSciNet  Google Scholar 

  • A. J. Czerniakiewicz 72,Automorphisms of a free associative algebra of rank 2, II, Trans. Amer. Math. Soc.171 (1972), 309–315.

    Article  MATH  MathSciNet  Google Scholar 

  • R. K. Dennis 70,Presentations for the elementary group, and the functor K 2, Thesis, Rice University, 1970.

  • W. J. Dicks 72,On one-relator associative algebras, J. London Math. Soc. (2)5 (1972), 249–252.

    Article  MATH  MathSciNet  Google Scholar 

  • W. J. Dicks 74,Idealizers in free algebras, Thesis, London University, 1974.

  • S. Eilenberg 74,Automata, languages and machines vol. A, New York, 1974.

  • W. Engel 62,Über die Derivationen eines Polynomringes, Math. Nachr.24 (1962), 275–280.

    Article  MATH  MathSciNet  Google Scholar 

  • I. Fischer and R. R. Struik 68,Nil algebras and periodic groups, Amer. Math. Monthly75 (1968), 611–623.

    Article  MATH  MathSciNet  Google Scholar 

  • J. L. Fisher 74,The Poset of skew fields generated by a free algebra, Proc. Amer. Math. Soc.42 (1974) 33–35.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Fliess 70,Transductions algébriques, R.I.R.O.R-1 (1970), 109–125.

    MathSciNet  Google Scholar 

  • M. Fliess 71,Deux applications de la représentation matricielle d’une série rationnelle non-commutative, J. Algebra19 (1971), 344–353.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Fliess 72,Sur certaines familles des séries formelles, Thesis, University of Paris VII, 1972.

  • M. Fliess 74a,Matrices de Hankel, to appear.

  • M. Fliess 74b,Sur divers produits de séries formelles, Bull. Soc. Math. France, to appear.

  • A. Fröhlich 63,Baer invariants of algebras, Trans. Amer. Math. Soc.109 (1963), 221–244.

    Article  MATH  MathSciNet  Google Scholar 

  • P. Gabriel 62,Des catégories abéliennes Bull. Soc. Math. France90 (1962), 323–448.

    MATH  MathSciNet  Google Scholar 

  • S. M. Gersten 65,Whitehead groups of free associative algebras, Bull. Amer. Math. Soc.71 (1965), 157–159.

    MATH  MathSciNet  Google Scholar 

  • S. M. Gersten 73,Higher K-theory of rings, Proc. of conference on algebraicK-theory at the Battelle Institute in Seattle, Wash., 1972, Lecture Notes in Math. vol. 341, Berlin 1973.

  • S. M. Gersten 74,K- theory of free rings, Comm. Algebra1 (1974), 39–64.

    MATH  MathSciNet  Google Scholar 

  • S. Ginsburg 66,The mathematical theory of context-free languages, New York, 1966.

  • E. S. Golod and I. R. Šafarevič 64,On class field towers, Izv. Akad. Nauk SSSR Ser. Mat.28 (1964), 262–272; Amer. Math. Soc. Transl. (2)48 (1965), 91–102.

    Google Scholar 

  • M. I. Graev and A. A. Kirillov 68,Theory of group representations, (Russian), Proc. ICM Moscow 1966, 1968, pp. 373–379.

  • A. Grothendieck and J. Dieudonné 71,Eléments de Géométrie Algébrique I, Grundlehren d. math. Wiss., Vol. 166, Berlin, 1971.

  • M. Hall 59,The theory of groups, New York, 1959.

  • M. Hochster 69,Prime ideal structure in commutative rings, Trans. Amer. Math. Soc.142 (1969), 43–60.

    Article  MATH  MathSciNet  Google Scholar 

  • K. H. Hofmann 72,Representations of algebras by continuous sections, Bull. Amer. Math. Soc.78 (1972), 291–373.

    MATH  MathSciNet  Google Scholar 

  • N. Jacobson 62,Lie algebras, New York and London, 1962.

  • A. V. Jategaonkar 69,Ore domains and free algebras, Bull. London Math. Soc.1 (1969), 45–46.

    Article  MATH  MathSciNet  Google Scholar 

  • B. Jónsson 56,Universal relational systems, Math. Scand.4 (1956), 193–208.

    MATH  MathSciNet  Google Scholar 

  • B. Jónsson 60,Homogeneous universal relational systems, Math. Scand.8 (1960), 137–142.

    MATH  MathSciNet  Google Scholar 

  • T. de W. Jooste 71,Derivations in free power series rings and free associative algebras, Thesis, London University, 1971.

  • H. W. E. Jung 42,Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math.184 (1942), 161–174.

    MATH  MathSciNet  Google Scholar 

  • R. Jungen 31,Sur les séries de Taylor n’ayant que des singularités algébrico-logarithmiques sur leur cercle de convergence, Comment. Math. Helv.3 (1931), 266–306.

    Article  MATH  MathSciNet  Google Scholar 

  • S. C. Kleene 56,Representation of events in nerve sets, in: Automata Studies, C. E. Shannon and J. McCarthy (eds.) Princeton, 1956, pp. 3–40.

  • A. A. Klein 69,Necessary conditions for embedding rings into fields, Trans. Amer. Math. Soc.137 (1969), 141–151.

    Article  MATH  MathSciNet  Google Scholar 

  • M. A. Knus 68,Homology and homomorphisms of rings, J. Algebra9 (1968), 274–284.

    Article  MATH  MathSciNet  Google Scholar 

  • E. G. Koševoi 70,On certain associative algebras with transcendental relations (Russian), Algebra i Logika9 (1970), 520–529.

    MathSciNet  Google Scholar 

  • E. G. Koševoi 71,On pure subalgebras of free associative algebras (Russian), Algebra i Logika10 (1971), 183–187.

    MathSciNet  Google Scholar 

  • W. van der Kulk 53,On polynomial rings in two variables, Nieuw Arch. Wisk. (3)1 (1953), 33–41.

    MATH  Google Scholar 

  • J. P. Labute 67,Algèbres de Lie et pro-p-groupes définis par une seule relation, Invent. Math.4 (1967), 142–158.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Lambek and G. Michler 73,The torsion theory at a prime ideal of a right Noetherian ring, J. Algebra25 (1973), 364–389.

    Article  MATH  MathSciNet  Google Scholar 

  • D. R. Lane 74,Fixed points of affine Cremona transformations of the plane over an algebraically closed fields, Amer. J. Math.

  • J. Lewin 69,Free modules over free algebras and free group algebras: the Schreier technique, Trans. Amer. Math. Soc.145 (1969), 455–465.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Lewin 73,On some infinitely presented associative algebras and an example of L. Small J. Austral. Math, Soc.16 (1973), 290–293.

    MATH  MathSciNet  Google Scholar 

  • J. Lewin 74a,A matrix representation for free associative algebras I, II, Trans. Amer. Math Soc.188 (1974), 293–308, 309–317.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Lewin 74b,Fields of fractions for group algebras of free groups, Trans. Amer. Math. Soc.192 (1974) 339–346.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Lewin and T. Lewin 68,On ideals of free associative algebras generated by a single element, J. Algebra8 (1968), 248–255.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Macintyre 73,The word problem for division rings, J. Symbolic Logic38 (1973) 428–436,

    Article  MATH  MathSciNet  Google Scholar 

  • A. Macintyre 74,On algebraically closed division rings, Ann. Math. Logic (in press).

  • W. Magnus 39,On a theorem of Marshall Hall, Ann. of Math.40 (1939), 764–776.

    Article  MathSciNet  Google Scholar 

  • W. Magnus A. Karrass, and D. Solitar, 66,Combinatorial Group Theory, New York, 1966.

  • L. G. Makar-Limanov 70,The automorphisms of the free algebra with two generators, (Russian), Funkcional. Anal. i Prilozhen.4 (1970), 107–108.

    MATH  MathSciNet  Google Scholar 

  • A. I. Mal’cev 48,On the embedding of group algebras in division algebras, Dokl. Akad. Nauk SSSR60 (1948), 1499–1501.

    MathSciNet  Google Scholar 

  • A. I. Mal’cev 73,Algebraic Systems, Grundlehren d. math. Wiss. Vol.192, Berlin, 1973.

  • S. Moran 73,Some subalgebra theorems, J. Algebra,29 (1973) 366–371.

    Article  Google Scholar 

  • D. C. Murdoch and F. M. J. van Oystaeyen 75,Non-commutative localization and varieties, to appear.

  • B. H. Neumann 49,On ordered division rings, Trans. Amer. Math. Soc.66 (1949), 202–252.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Nivat 68,Transduction des langages de Chomsky, Ann. Inst. Fourier (18)1 (1968), 339–456.

    MathSciNet  Google Scholar 

  • M. Nivat 70,Séries rationnelles et algébriques en variables non-commutatives, Cours du DEA, 1969/70.

  • C. Procesi 66,A non-commutative Hilbert Nullstellensatz, Rend. Mat. e Appl. V,25 (1966), 17–25.

    MathSciNet  Google Scholar 

  • C. Procesi 68,Sulle identità delle algebre semplici, Rend. Circ. Mat. Palermo, (2)17 (1968), 13–18.

    MATH  MathSciNet  Google Scholar 

  • D. P. Robbins 71,Jordan elements in a free associative algebra I, J. Algebra19 (1971), 354–378.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Robinson 70,Forcing in model theory, Symposia Math.V (1970), 69–82.

    Google Scholar 

  • A. Robinson 71,On the notion of algebraic closedness for non-commutative groups and fields, J. Symb. Logic.36 (1971), 441–444.

    Article  MATH  Google Scholar 

  • M.-P. Schützenberger 61,On the definition of a family of automata, Information and Control4 (1961), 245–270.

    Article  MATH  MathSciNet  Google Scholar 

  • M.-P. Schützenberger 62,On a theorem of R. Jungen, Proc. Amer. Math. Soc.13 (1962), 885–890.

    Article  MATH  MathSciNet  Google Scholar 

  • E. Shamir 67,A representation theorem for algebraic and context-free power series in noncommuting variables, Information and Control11 (1967), 239–254.

    Article  MATH  MathSciNet  Google Scholar 

  • S. S. Shatz 72,Profinite Groups, Arithmetic and Geometry, Princeton, 1972.

  • J. R. Silvester 73,On the K 2 of a free associative algebra, Proc. London Math. Soc. (3)26 (1973), 35–56.

    Article  MATH  MathSciNet  Google Scholar 

  • A. I. Širšov 62,Some algorithmic problems for Lie algebras (Russian), Sibirsk. Mat. Ž.3 (1962), 292–296.

    MathSciNet  Google Scholar 

  • L. A. Skornyakov 65,On Cohn rings (Russian), Algebra i Logika (3)4 (1965), 5–30.

    MATH  MathSciNet  Google Scholar 

  • M. E. Sweedler 69,Hopf Algebras, New York, 1969.

  • J. L. Taylor 73,Functions of several non-commuting variables, Bull. Amer. Math. Soc.79 (1973), 1–34.

    Article  MATH  MathSciNet  Google Scholar 

  • W. H. Wheeler 72,Algebraically closed division rings, forcing and the analytical hierarchy, Thesis, Yale University, 1972.

  • J. H. C. Whitehead 36,On equivalent sets of elements in a free group, Ann. of Math.37 (1936), 782–800.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bedford College, Regents Park, London, England

    P. M. Cohn

Authors
  1. P. M. Cohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

To the memory of J. Levitzki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cohn, P.M. Progress in free associative algebras. Israel J. Math. 19, 109–151 (1974). https://doi.org/10.1007/BF02756628

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02756628

Keywords

Search

Navigation