The classical left regular left quotient ring of a ring and its semisimplicity criteria

2015/04/27 by V. V. Bavula, Bavula, V. V.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.RA #msc:16P20 #msc:16P50 #msc:16P60 #msc:16U20

paper · pdf · doi:10.48550/arxiv.1504.07257

22 pages

arxiv created 2015/04/27 · arxiv updated 2015/04/29

Abstract

Let R be a ring, \CC_R and \pCCR be the set of regular and left regular elements of R (\CC_R⊆ \pCCR). Goldie's Theorem is a semisimplicity criterion for the classical left quotient ring Q_l,cl(R):=\CC_R^-1R. Semisimplicity criteria are given for the classical left regular left quotient ring 'Q_l,cl(R):=\pCCR^-1R. As a corollary, two new semisimplicity criteria for Q_l,cl(R) are obtained (in the spirit of Goldie).

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