Characterizations of ordered intra $k$-regular semirings by ordered $k$-ideals

Pakorn Palakawong na Ayutthaya; Bundit Pibaljommee

doi:10.4134/CKMS.c160271

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

QR
Code

Article

HOME

ALL ARTICLES

View

Commun. Korean Math. Soc. 2018; 33(1): 1-12

Online first article January 9, 2018 Printed January 31, 2018

https://doi.org/10.4134/CKMS.c160271

Characterizations of ordered intra $k$-regular semirings by ordered $k$-ideals

Pakorn Palakawong na Ayutthaya, Bundit Pibaljommee

Khon Kaen University, Centre of Excellence in Mathematics CHE

Abstract

Go to

Abstract

We introduce the notion of ordered intra $k$-regular semirings, characterize them using their ordered $k$-ideals and prove that an ordered semiring $S$ is both ordered $k$-regular and ordered intra $k$-regular if and only if every ordered quasi $k$-ideal or every ordered $k$-bi-ideal of $S$ is ordered $k$-idempotent.

Keywords: ordered semiring, ordered $k$-regular, ordered $k$-ideal

MSC numbers: Primary 06F25, 16Y60