Regular $P.I.$-rings
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- by E. P. Armendariz and Joe W. Fisher
- Proc. Amer. Math. Soc. 39 (1973), 247-251
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313305-3
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Abstract:
For a ring $R$ which satisfies a polynomial identity we show that the following are equivalent: (1) $R$ is von Neumann regular, (2) each two-sided ideal of $R$ is idempotent, and (3) each simple left (right) $R$-module is injective. We show that a P.I.-ring $R$ is left perfect if and only if all left $R$-modules have maximal submodules and $R$ has no infinite sets of orthogonal idempotents.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 247-251
- MSC: Primary 16A38; Secondary 16A30
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313305-3
- MathSciNet review: 0313305