A coefficient ring for finite non-commutative rings

Clark, W. Edwin

doi:10.1090/S0002-9939-1972-0294411-8

A coefficient ring for finite non-commutative rings
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by W. Edwin Clark PDF

Proc. Amer. Math. Soc. 33 (1972), 25-28 Request permission

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

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