A simplification of Morita's construction of total right rings of quotients for a class of rings

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dc.creatorVas, Lia
dc.date2007-02-18
dc.date.accessioned2026-07-07T07:47:34Z
dc.date.available2026-07-07T07:47:34Z
dc.descriptionThe total right ring of quotients $Q_{\mathrm{tot}}^r(R),$ sometimes also called the maximal flat epimorphic right ring of quotients or right flat epimorphic hull, is usually obtained as a directed union of a certain family of extension of the base ring $R$. In [K. Morita, Flat modules, injective modules and quotient rings, Math. Z. 120 (1971) 25--40], $Q_{\mathrm{tot}}^r(R)$ is constructed in a different way, by transfinite induction on ordinals. Starting with the maximal right ring of quotients $Q_{\mathrm{max}}^r(R)$, its subrings are constructed until $Q_{\mathrm{tot}}^r(R)$ is obtained. Here, we prove that Morita's construction of $Q_{\mathrm{tot}}^r(R)$ can be simplified for rings satisfying condition (C) that every subring of the maximal right ring of quotients $Q^r_{\mathrm{max}}(R)$ containing $R$ is flat as a left $R$-module. We illustrate the usefulness of this simplification by considering the class of right semihereditary rings all of which satisfy condition (C). We prove that the construction stops after just one step and we obtain a simple description of $Q^r_{\mathrm{tot}}(R)$ in this case. Lastly, we study conditions that imply that Morita's construction ends in countably many steps.
dc.identifierhttps://arxiv.org/abs/math/0702526
dc.identifierhttp://arxiv.org/abs/math/0702526
dc.identifierL. Vas, A Simplification of Morita's Construction of Total Right Rings of Quotients for a Class of Rings, Journal of Algebra 304 (2006) no. 2, 989 - 1003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124209
dc.subjectRings and Algebras
dc.subject16S90, 16N80, 16E60
dc.titleA simplification of Morita's construction of total right rings of quotients for a class of rings
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