Semirings satisfying properties of distributive type
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- by Arif Kaya and M. Satyanarayana PDF
- Proc. Amer. Math. Soc. 82 (1981), 341-346 Request permission
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
- Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
- Mario Petrich, Introduction to semigroups, Merrill Research and Lecture Series, Charles E. Merrill Publishing Co., Columbus, Ohio, 1973. MR 0393206
Additional Information
- © Copyright 1981 American Mathematical Society
- 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