Research Article

Semiring with Identity

by  C. Venkata Lakshmi, T. Vasanthi
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 88 - Issue 17
Published: February 2014
Authors: C. Venkata Lakshmi, T. Vasanthi
10.5120/15442-3600
PDF

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 },
                        year    = { 2014 },
                        volume  = { 88 },
                        number  = { 17 },
                        pages   = { 5-7 },
                        doi     = { 10.5120/15442-3600 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2014
                        %A C. Venkata Lakshmi
                        %A T. Vasanthi
                        %T Semiring with Identity%T 
                        %J International Journal of Computer Applications
                        %V 88
                        %N 17
                        %P 5-7
                        %R 10.5120/15442-3600
                        %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
  • 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"
  • 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).
  • J. Hanumanthachari and K. Venuraju , "The additive semigroup structure of semirings". Mathematics seminar notes, Vol. 11(1983),381-386.
  • M. Satyanarayana – "On the additive semigroup of ordered semirings",Semigroup forum vol. 31 (1985), 193-199
Index Terms
Computer Science
Information Sciences
No index terms available.
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.

Powered by PhDFocusTM