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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
DOI: https://doi.org/10.1090/S0002-9939-1981-0612715-9
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] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1948. MR 0029876 (10:673a)
  • [2] M. Petrich, Introduction to semigroups, Merrill, Columbus, Ohio, 1973. MR 0393206 (52:14016)

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Additional Information

DOI: https://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

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