Prime and Maximal Ideals in Ternary Semigroups

P  Bindu; Y  Sarala; D  Madhusudhana Rao  and G  Jaya Lalitha

doi:10.17485/ijst/2015/v8i14/59162

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Prime and Maximal Ideals in Ternary Semigroups

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i14/59162

Year: 2015, Volume: 8, Issue: 14, Pages: 1-4

Original Article

Prime and Maximal Ideals in Ternary Semigroups

P. Bindu¹, Y. Sarala^2*, D. Madhusudhana Rao³ and G. Jaya Lalitha¹

¹Department of Mathematics, KL University, Guntur - 522502, Andhra Pradesh, India

²Faculty of Mathematics, Department of Mathematics, KL University, Guntur – 522502, Andhra Pradesh, India; [email protected]

³ Faculty of Mathematics, Department of Mathematics, VSR and NVR College, Tenali - 522201, Andhra Pradesh, India; [email protected]; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This paper deals with prime and maximal ideals in ternary semigroup. In this paper we shall study the intersection of all prime ideals and intersection of all maximal ideals in a (non-commutative) ternary semigroup T. In particular we give a rather general necessary and sufficient condition in order that the set of all maximal ideals coincides with the set of all prime ideals.

Keywords: Maximal Ideal of a Ternary Semigroup, Prime Ideal