Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A coefficient ring for finite non-commutative rings


Author: W. Edwin Clark
Journal: Proc. Amer. Math. Soc. 33 (1972), 25-28
MSC: Primary 16A44
MathSciNet review: 0294411
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every finite p-ring R contains a unique (up to isomorphism) subring S such that $ 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))$ where $ f(x)$ is monic and irreducible modulo p.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A44

Retrieve articles in all journals with MSC: 16A44


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294411-8
Keywords: Coefficient ring, Wedderburn-Malcev Theorem, Galois ring
Article copyright: © Copyright 1972 American Mathematical Society