1981•Proceedings of the American Mathematical SocietyRequires access
Semirings satisfying properties of distributive type
Arif Kaya, M. Satyanarayana
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Abstract
Any distributive lattice admits a semiring structure in a natural way and this particular semiring satisfies some new distributive properties. The purpose of this note is to study whether a semiring with some or all of these new distributive properties admits the natural distributive lattice structure, and thus obtain Birkhoff’s theorem as a corollary. Furthermore, characterizations of semirings satisfying some or all of these new distributive properties are obtained.