Some Special Classes of Semirings
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
- Arif Kaya and M. Satyanarayana, "Semirings satisfying properties of distributive type", Proceeding of the American Mathematical Society, Volume 82, Number 3, July 1981.
- Jonathan S. Golan, " Semirings and their Applications".
- 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;