Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Semirings satisfying properties of distributive type


Authors: Arif Kaya and M. Satyanarayana
Journal: Proc. Amer. Math. Soc. 82 (1981), 341-346
MSC: Primary 16A78; Secondary 06D05
MathSciNet review: 612715
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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.


References [Enhancements On Off] (What's this?)

  • [1] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, revised edition, American Mathematical Society, New York, N. Y., 1948. MR 0029876
  • [2] Mario Petrich, Introduction to semigroups, Charles E. Merrill Publishing Co., Columbus, Ohio, 1973. Merrill Research and Lecture Series. MR 0393206

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612715-9
Keywords: Band, rectangular band, left zero semigroup, distributive lattice
Article copyright: © Copyright 1981 American Mathematical Society