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Regular $P.I.$-rings

1973; American Mathematical Society; Volume: 39; Issue: 2 Linguagem: Inglês

10.1090/s0002-9939-1973-0313305-3

1088-6826

Efraim P. Armendariz, Joe W. Fisher,

Advanced Topics in Algebra

For a ring R R which satisfies a polynomial identity we show that the following are equivalent: (1) R R is von Neumann regular, (2) each two-sided ideal of R R is idempotent, and (3) each simple left (right) R R -module is injective. We show that a P.I.-ring R R is left perfect if and only if all left R R -modules have maximal submodules and R R has no infinite sets of orthogonal idempotents.