DM-GAA

Article in press

Authors:

P. Summaprab

Pisan Summaprab

Department of Mathematics, Rajamangala University of Technology Isan,
Khon Kaen Campus, Khon Kaen 40000, Thailand

Title:

On $B^{*}$-pure ordered semigroup

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2022-06-23 , Revised: 2022-10-18 , Accepted: 2022-10-26 , Available online: 2024-02-08 , https://doi.org/10.7151/dmgaa.1449

Abstract:

We introduce the concept of $B^{*}$-pure ordered semigroup, and give some properties of $B^{*}$-pure ordered semigroups.

Keywords:

semigroup, ordered semigroup, $B$-pure, normal, weakly commutative, archimedean, semilattice, bi-ideal

References:

K. Hansda, Idempotent ordered semigroups (2017).
arXiv: 1706.08213v1
L. Fuchs, Partially ordered Algebraic Systems (Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc, Reading, Mass.-Palo Alto, Calif.-London Pergamon Press, 1963).
N. Kuroki, On $B^{*}$-pure semigroups, Acta Math. Hung. 43 (1984) 295–298.
N. Kehayopulu, M. Tsingelis, On weakly commutative ordered semigroups, Semigroup Forum 56 (1998) 32–35.
https://doi.org/10.1007/s00233-002-7002-6
N. Kehayopulu, On completely regular poe-semigroups, Math. Japonica 37 (1992) 123–130.
N. Kehayopulu, On weakly commutative poe-semigroups, Semigroup Forum 34 (1987) 367–370.
https://doi.org/10.1007/BF02573174
N. Kehayopulu, On regular duo ordered semigroups, Math. Japonica 37 (1992) 535–540.
T. Changphas, An Introduction to Ordered Semigroups (Lecture Note, 2016).
T. Changphas, P. Kummoon, Purity of ideals and generalized ideals on ordered semigroups, Quasigroups and Related systems 26 (2018) 185–196.
T. Changphas, P. Luangchaisri and R. Mazurek, On right chain ordered semigroups, Semigroup Forum 96 (2018) 523–535.
https://doi.org/10.1007/s00233-017-9896-z