Skip to main content
SpringerLink
Log in

On invariant additive subgroups

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

Abstract

Suppose thatR is a prime ring with the centerZ and the extended centroidC. An additive subgroupA ofR is said to be invariant under special automorphisms if (1+t)A(1+t)−1 ⊆A for allt ∈R such thatt 2=0. Assume thatR possesses nontrivial idempotents. We prove: (1) If chR ≠ 2 or ifRC ≠C 2, then any noncentral additive subgroup ofR invariant under special automorphisms contains a noncentral Lie ideal. (2) If chR=2,RC=C 2 andC ≠ {0, 1}, then the following two conditions are equivalent: (i) any noncentral additive subgroup invariant under special automorphisms contains a noncentral Lie ideal; (ii) there isα ∈Z / {0} such thatα 2 Z ⊆ {β 2:β ∈Z}.

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

Similar content being viewed by others

References

  1. S. A. Amitsur,Invariant submodules of simple rings, Proc. Am. Math. Soc.7 (1956), 987–989.

    Article  MathSciNet  Google Scholar 

  2. I. N. Herstein,Topics in Ring Theory, Chicago Lecture Notes in Mathematics, Univ. of Chicago Press, Chicago, 1969.

    MATH  Google Scholar 

  3. I. N. Herstein,Rings with Involution, Chicago Lecture Notes in Mathematics, Univ. of Chicago Press, Chicago, 1976.

    MATH  Google Scholar 

  4. I. N. Herstein,A theorem on invariant subrings, J. Algebra83 (1983), 26–32.

    Article  MATH  MathSciNet  Google Scholar 

  5. V. K. Kharchenko,Differential identities of prime rings, Algebra i Logika17 (1978), 155–167 (English translation).

    Article  MATH  Google Scholar 

  6. C. Lanski and S. Montgomery,Lie structure of prime rings of characteristic 2, Pacific J. Math.42 (1972), 117–136.

    MATH  MathSciNet  Google Scholar 

  7. W. S. Martindale,Prime rings satisfying a generalized polynomial identity, J. Algebra12 (1969), 576–584.

    Article  MATH  MathSciNet  Google Scholar 

  8. E. C. Posner,Derivations in prime rings, Proc. Am. Math. Soc.8 (1957), 1093–1100.

    Article  MathSciNet  Google Scholar 

  9. O. Zariski and P. Samuel,Commutative Algebra, Vol. 1, D. Van Nostrand Company, Inc., Princeton, N.J., 1958.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, Taiwan 107, Republic of China

    C. L. Chuang

Authors
  1. C. L. Chuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chuang, C.L. On invariant additive subgroups. Israel J. Math. 57, 116–128 (1987). https://doi.org/10.1007/BF02769465

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02769465

Keywords

Search

Navigation