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One theorem of Cohn

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Abstract

Let F be the field of algebraic functions of one variable over the field of constants k, v be a point of field F/k, and Av be the ring of functions not having poles outside point v. It is proved that Av is a GE2-ring if and only if it coincides with the ring k[X] of polynomials of one variable over field k.

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Literature cited

  1. L. N. Vasershtein, “On the group SL2 over Dedekind rings of arithmetic type,” Mat. Sb.,89, No. 2, 313–322 (1972).

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  2. P. M. Cohn, “On the structure of the GL2 of a ring,” Publ. Math. Inst. Hautes Etudes Sci., No. 30, 365–413 (1966).

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  3. C. Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, Am. Math. Soc., Providence, Rhode Island (1951; reprinted 1971).

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Authors
  1. A. A. Suslin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 127–130, 1976.

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Suslin, A.A. One theorem of Cohn. J Math Sci 17, 1801–1803 (1981). https://doi.org/10.1007/BF01091767

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  • DOI: https://doi.org/10.1007/BF01091767

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