Article
Kyungpook Mathematical Journal 2022; 62(1): 29-41
Published online March 31, 2022
Copyright © Kyungpook Mathematical Journal.
Left Regular and Left Weakly Regular n-ary Semigroups
Patchara Pornsurat and Bundit Pibaljommee*
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
e-mail : p.patchara@kkumail.com and banpib@kku.ac.th
Received: July 13, 2021; Revised: November 2, 2021; Accepted: November 15, 2021
We study the concept of a quasi-ideal and a generalized bi-ideal of an n-ary semigroup; give a construction of the quasi-ideal of an n-ary semigroup generated by its nonempty subset; and introduce the notions of regularities, namely, a left regularity and a left weakly regularity. Moreover, the notions of a right regularity, a right weak regularity and a complete regularity are given. Finally, characterizations of these regularities are presented.
Keywords: n-ary semigroup, left regular, right regular, quasi-ideal