Characterizations of ordered h-regular semirings by ordered h-ideals

Anjum R., Ullah S., Chu Y., Munir M., KAUSAR N., Kadry S.

AIMS Mathematics, vol.5, no.6, pp.5768-5790, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.3934/math.2020370
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5768-5790
  • Keywords: Ordered h-ideal, Ordered h-regular, Ordered semiring, Semiring
  • Yıldız Technical University Affiliated: Yes

Abstract

The objective of this paper is to study the ordered h-regular semirings by the properties of their ordered h-ideals. It is proved that each h-regular ordered semiring is an ordered h-regular semiring but the converse does not follow. Important theorems relating to basic properties of the operator clousre and h-regular semirings are given. It is also proved that each regular ordered semiring is an ordered h-regular semiring but the converse does not hold. The classifications of the left and the right ordered h-regular semirings and the left and the right ordered h-weakly regular semirings are also presented.