ON IDEALS OF A CLASS OF SEMILATTICE ORDERED
SEMIRINGS

M. Siva Mala; P. V. Srinivasa Rao

doi:https://doi.org/10.14445/22315373/IJMTT-V38P524

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 38 | Number 3 | Year 2016 | Article Id. IJMTT-V38P524 | DOI : https://doi.org/10.14445/22315373/IJMTT-V38P524

ON IDEALS OF A CLASS OF SEMILATTICE ORDERED SEMIRINGS

M. Siva Mala, P. V. Srinivasa Rao

Abstract

The class of lattice ordered semirings studied by P. Ranga Rao[5] in 1981 is a common abstraction of lattice ordered rings and Boolean rings. In 2007, we introduced the notion of a semilattice ordered semirings (slsemirings)[3] as a generalization of lattice ordered semirings. In this paper, we introduce the notions of nilpotent, prime and irreducible ideals to a class of semilattice ordered semirings and obtain the characteristics of them.

Keywords

SEMILATTICE ORDERED SEMIRINGS

References

[1] G. Birkho, Lattice theory. Amer. Math. Soc. Colloq. Publ., XXV, 3rd edition, 1973.
[2] W. C. Nemitz, Implicative Semilattice. Trans. Amer. Math. Soc., 117(1965), 128{142.
[3] N. Prabhakara Rao and M. Siva Mala,On a Class of Semilattice Ordered Semirings. Acta Ciencia Indica, XXXIV M(2008), no. 1, 345{350.
[4] P. V. Ramana Murthy, Semi Brouwerian Algebra. Jour. Aust. Math. Soc., XVII(1974), no. 3, 293{302.
[5] P. Ranga Rao, Lattice Ordered Semirings. Mathematics Seminar Notes, 9(1981), 119{149.
[6] P. S. Rema, Boolean metrization and topological spaces. Math. Japonicae, 9(1964), 19{30.
[7] K. L. N. Swamy, Dually Residuated Lattice Ordered Semigroups. Math. Annalen., 159(1965), 105-114.

Citation :

M. Siva Mala, P. V. Srinivasa Rao, "ON IDEALS OF A CLASS OF SEMILATTICE ORDERED SEMIRINGS," International Journal of Mathematics Trends and Technology (IJMTT), vol. 38, no. 3, pp. 138-143, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V38P524