Research Article

Semigroup Forum

, Volume 24, Issue 1, pp 231-254

First online:

Seminearrings, seminearfields and their semigroup-theoretical background

  • Hanns Joachim WeinertAffiliated withInstitut für Mathematik, Technische Universität Clausthal

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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.