A coefficient ring for finite non-commutative rings-Reference-Cited by-同舟云学术

A coefficient ring for finite non-commutative rings

Published:1972 Issue:1 Volume:33 Page:25-28
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Clark W. Edwin

Abstract

We prove that every finite p-ring R contains a unique (up to isomorphism) subring S such that S / p S ≅ R / rad R S/pS \cong R/{\operatorname {rad}}\;R . S is shown to be a direct sum of full matrix rings over rings of the form Z p n [ x ] / ( f ( x ) ) {Z_{{p^n}}}[x]/(f(x)) where f ( x ) f(x) is monic and irreducible modulo p.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-033-01/S0002-9939-1972-0294411-8/S0002-9939-1972-0294411-8.pdf

Reference6 articles.

1. Finite chain rings;Clark, W. Edwin;Abh. Math. Sem. Univ. Hamburg,1973

2. Pure and Applied Mathematics, Vol. XI;Curtis, Charles W.,1962

3. Separable algebras over commutative rings;Janusz, G. J.;Trans. Amer. Math. Soc.,1966

4. Algebraische Theorie der Ringe. II;Krull, Wolfgang;Math. Ann.,1924

5. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 46;Krull, Wolfgang,1968

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