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S-sets and semigroups of quotients

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Abstract

During the last two decades, a good deal of work has been conducted on S-sets and semigroups of quotients, establishing several concepts and results which are more or less analogous to the classicalas well as ring-theoretical ones. Clearly there are different (and sometimes, we feel, too restrictive) assumptions in these papers, in particular on the semigroups S and on the S-sets under consideration, and various notations need to be unified. Generalizing diverging dispositions, we try to give a self-contained survey of the most fundamental parts (and other considerable parts) of these investigations, and add some new results. A forthcoming paper will deal with S-semimodules over semirings S, including some relationships with rings and modules.

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  1. Institut für Mathematik, Technische Universität Clausthal, D-3392, Clausthal-Zellerfeld, Germany

    H. J. Weinert

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Weinert, H.J. S-sets and semigroups of quotients. Semigroup Forum 19, 1–78 (1980). https://doi.org/10.1007/BF02572502

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