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Some Special Classes of Semirings

C. Venkata Lakshmi, T. Vasanthi Published in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2014
© 2014 by IJAIS Journal
10.5120/ijais14-451093
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  1. Venkata C Lakshmi and T Vasanthi. Article: Some Special Classes of Semirings. International Journal of Applied Information Systems 6(8):27-29, February 2014. BibTeX

    @article{key:article,
    	author = "C. Venkata Lakshmi and T. Vasanthi",
    	title = "Article: Some Special Classes of Semirings",
    	journal = "International Journal of Applied Information Systems",
    	year = 2014,
    	volume = 6,
    	number = 8,
    	pages = "27-29",
    	month = "February",
    	note = "Published by Foundation of Computer Science, New York, USA"
    }
    

Abstract

In this paper, we discuss the structure of some special classes of semirings . Here the properties of Viterbi semirings; PRD semirings satisfying the identity ab + a = a, for all a, b in S and semirings satisfying the identity a + ab + a = a, for all a, b in S are studied. We proved that (S, +, •) is a semiring satisfying the identity a + ab + a = a, in which if S contains the multiplicative identity which is also an additive identity, then S is a multiplicatively subidempotent semiring.

Reference

  1. Arif Kaya and M. Satyanarayana, "Semirings satisfying properties of distributive type", Proceeding of the American Mathematical Society, Volume 82, Number 3, July 1981.
  2. Jonathan S. Golan, " Semirings and their Applications".
  3. Jonathan S. Golan, " Semirings and Affine Equations over Them : Theory and Applications". Kluwer Academic.

Keywords

Band; Left (Right) singular; PRD; Viterbi semiring; multiplicatively subidempotent; Weak commutative;