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Seminearrings, seminearfields and their semigroup-theoretical background

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Abstract

In this paper we deal with some basic properties of seminearrings (S,+,·), in particular with respect to multiplicative cancellativity (§2) and to seminearfields (§3, §4). All seminearrings of order 2 are listed in §5. In general, we do not assume that (S,+) is associative. Moreover, we present most of our results as consequences of corresponding statements on semigroups (S,·). Clearly, all results apply to semirings and nearrings, particularly to those with associative addition, and some of them will be new also in this context.

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Authors and Affiliations

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

    Hanns Joachim Weinert

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  1. Hanns Joachim Weinert
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Communicated by B. M. Schein

Dedicated to Professor L. M. Gluskin on his 60th birthday

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Weinert, H.J. Seminearrings, seminearfields and their semigroup-theoretical background. Semigroup Forum 24, 231–254 (1982). https://doi.org/10.1007/BF02572770

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  • DOI: https://doi.org/10.1007/BF02572770

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