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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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 25-28
- MSC: Primary 16A44
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294411-8
- MathSciNet review: 0294411