Irreducible & Strongly Irreducible Bi-Ideals of Γ-So-Rings

Authors

  • Dr. P. V. Srinivasa Rao
  • Dr. M. Siva Mala

Keywords:

bi-ideal, prime bi-ideal, semiprime bi-ideal, irreducible bi-ideal, strongly irreducible bi-ideal, regular Γ-so-ring and intra-regular Γ-so-ring.

Abstract

The set of all partial functions over a set under a natural addition (disjoint-domain sum), functional composition and functional relation on them, forms a Γ-so-ring. In this paper we introduce the notions of irreducible bi-ideal, strongly irreducible bi-ideal and strongly prime bi-ideals of Γ-so-rings and we prove that a bi-ideal is strongly irreducible if and only if it is strongly prime in a class of Γ-so-rings.

Key words and phrases. bi-ideal, prime bi-ideal, semiprime bi-ideal, irreducible bi-ideal, strongly irreducible bi-ideal, regular Γ-so-ring and intra-regular Γ-so-ring.

1991 Mathematics Subject Classification. 16Y60

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Published

2025-05-18

How to Cite

Dr. P. V. Srinivasa Rao, & Dr. M. Siva Mala. (2025). Irreducible & Strongly Irreducible Bi-Ideals of Γ-So-Rings. Jordan Journal of Mathematics and Statistics, 12(1), 35–49. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/954

Issue

Vol. 12 No. 1 (2019)

Section

Articles