ON SOME PARTIAL ORDERS ON A CERTAIN SUBSET OF THE POWER SET OF RINGS

Dolinar G., Kuzma B., Marovt J., ÜNGÖR B.

GLASNIK MATEMATICKI, vol.55, no.2, pp.177-190, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.3336/gm.55.2.01
  • Journal Name: GLASNIK MATEMATICKI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.177-190
  • Keywords: Baer *-ring, sharp partial order, core partial order, star partial order, one-sided partial order, CORE PARTIAL ORDER, LEFT-STAR, INVERSES, SHARP
  • Ankara University Affiliated: Yes

Abstract

Let R be a ring with identity and let J(R) be a collection of subsets of R. such that their left and right annihilators are generated by the same idempotent. We extend the notion of the sharp, the left-sharp, and the right-sharp partial orders to J(R), present equivalent definitions of these orders, and study their properties. We also extend the concept of the core and the dual core orders to J(R), show that they are indeed partial orders when R. is a Baer *-ring, and connect them with one-sided sharp and star partial orders.