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arXiv · 1504.07257

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

V. V. Bavula
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Abstract

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

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V. V. Bavula. 2015-04-27. The classical left regular left quotient ring of a ring and its semisimplicity criteria. https://arxiv.org/abs/1504.07257

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