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

Rukhshanda Anjum; Saad Ullah; Yu Ming Chu; Mohammad Munir; Nasreen Kausar; Seifedine Kadry

doi:10.3934/math.2020370

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

Rukhshanda Anjum
, Saad Ullah
, Yu Ming Chu
, Mohammad Munir
, Nasreen Kausar
, Seifedine Kadry

The University of Lahore
Huzhou University
Changsha University of Science and Technology
Government Postgraduate College
University of Agriculture Faisalabad
Beirut Arab University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	5768-5790
Number of pages	23
Journal	AIMS Mathematics
Volume	5
Issue number	6
DOIs	https://doi.org/10.3934/math.2020370
State	Published - 2020
Externally published	Yes

Keywords

Ordered h-ideal
Ordered h-regular
Ordered semiring
Semiring

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10.3934/math.2020370

Cite this

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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.",

keywords = "Ordered h-ideal, Ordered h-regular, Ordered semiring, Semiring",

author = "Rukhshanda Anjum and Saad Ullah and Chu, \{Yu Ming\} and Mohammad Munir and Nasreen Kausar and Seifedine Kadry",

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AU - Anjum, Rukhshanda

AU - Ullah, Saad

AU - Chu, Yu Ming

AU - Munir, Mohammad

AU - Kausar, Nasreen

AU - Kadry, Seifedine

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Ordered h-ideal

KW - Ordered h-regular

KW - Ordered semiring

KW - Semiring

UR - https://www.scopus.com/pages/publications/85089119469

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DO - 10.3934/math.2020370

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SN - 2473-6988

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SP - 5768

EP - 5790

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 6

ER -

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

Abstract

Keywords

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