On Semilocal Rings And Finitely Generated Projective Modules
Abstract
We establish the equivalence between the existence of a cyclic projective right C-module P such that P/J (BP) is semisimple and BP is finitely generated (B = End (Pc)) and the existence of an idempotent element e in c such that trace (Pc) is finitely generated (and equals CeC) and C/S is semisimple where S is the intersection of all maximal left ideals of C not containing the trace ideal of Pc.
On Semilocal Rings And Finitely Generated Projective Modules
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On Semilocal Rings And Finitely Generated Projective Modules
الملخص
We establish the equivalence between the existence of a cyclic projective right C-module P such that P/J (BP) is semisimple and BP is finitely generated (B = End (Pc)) and the existence of an idempotent element e in c such that trace (Pc) is finitely generated (and equals CeC) and C/S is semisimple where S is the intersection of all maximal left ideals of C not containing the trace ideal of Pc.