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Proceedings of the American Mathematical Society

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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
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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?)

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Keywords: Coefficient ring, Wedderburn-Malcev Theorem, Galois ring
Article copyright: © Copyright 1972 American Mathematical Society

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