Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2019; 56(4): 829-839

Online first article July 9, 2019      Printed July 31, 2019

https://doi.org/10.4134/BKMS.b180635

Copyright © The Korean Mathematical Society.

Weakly prime ideals in commutative semigroups

D. D. Anderson, Sangmin Chun, Jason R. Juett

The University of Iowa; Chung-Ang University; Texas State University

Abstract

Let $S$ be a commutative semigroup with $0$ and 1. A proper ideal $P$ of $S$ is {\it weakly prime} if for $a,b \in S$, $0 \ne ab \in P$ implies $a \in P$ or $b \in P$. We investigate weakly prime ideals and related ideals of $S$. We also relate weakly prime principal ideals to unique factorization in commutative semigroups.

Keywords: weakly prime ideal, prime ideal, commutative semigroup

MSC numbers: 20M12, 20M14

Supported by: The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant no.NRF-2018R1D1A1B07046733)