Abstract
This chapter contains applications of the localizing functors, and quotient categories defined in the preceding chapter. The application 16.9 is to multiplicative subsets S of a ring R, and the corresponding (partial) ring of quotients R s with respect to S. Theorem 16.12 yields the Johnson maximal right quotient ring \(\widehat R\) of a right neat ring R (cf. Chapter 19). When R is semiprime, and satisfies the \({(acc)^ \bot }\) and (acc)⊕, then \(\widehat R\) is the classical right quoring.
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© 1973 Springer-Verlag, Berlin · Heidelberg
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Faith, C. (1973). Torsion Theories, Radicals, and Idempotent, Topologizing, and Multiplicative Sets. In: Algebra. Die Grundlehren der mathematischen Wissenschaften, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80634-6_18
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DOI: https://doi.org/10.1007/978-3-642-80634-6_18
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