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Semiring with Identity

by C. Venkata Lakshmi, T. Vasanthi
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 88 - Number 17
Year of Publication: 2014
Authors: C. Venkata Lakshmi, T. Vasanthi
10.5120/15442-3600

C. Venkata Lakshmi, T. Vasanthi . Semiring with Identity. International Journal of Computer Applications. 88, 17 ( February 2014), 5-7. DOI=10.5120/15442-3600

@article{ 10.5120/15442-3600,
author = { C. Venkata Lakshmi, T. Vasanthi },
title = { Semiring with Identity },
journal = { International Journal of Computer Applications },
issue_date = { February 2014 },
volume = { 88 },
number = { 17 },
month = { February },
year = { 2014 },
issn = { 0975-8887 },
pages = { 5-7 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume88/number17/15442-3600/ },
doi = { 10.5120/15442-3600 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:07:51.951770+05:30
%A C. Venkata Lakshmi
%A T. Vasanthi
%T Semiring with Identity
%J International Journal of Computer Applications
%@ 0975-8887
%V 88
%N 17
%P 5-7
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we study the properties of semiring with identity ab + a = a and also study the properties of ordered semiring satisfying the identity ab + a = a, for all a, b in S. This paper contains mainly two sections. In section 1, the structure of semirings satisfying the identity ab + a = a, for all a, b in S are studied. In section 2, we characterize totally ordered semirings satisfying the identity ab + a = a, for all a, b in S.

References
  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. J. Hanumanthachari and D. Umamaheswara Reddy, "A note on maximal and minimal elements in totally ordered semirings". SEA. Bull. Math. Vol. 13. No. 2 (1989).
  4. J. Hanumanthachari and K. Venuraju , "The additive semigroup structure of semirings". Mathematics seminar notes, Vol. 11(1983),381-386.
  5. M. Satyanarayana – "On the additive semigroup of ordered semirings",Semigroup forum vol. 31 (1985), 193-199
Index Terms

Computer Science
Information Sciences

Keywords

Left regular semigroup PRD E – inverse semigroup Quasi separative Positively totally ordered (p. t. o. ) Negatively totally ordered (n. t. o. ) Non - negatively ordered Non - positively totally ordered.

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