Weakly prime ideals in commutative semigroups
Bull. Korean Math. Soc. 2019 Vol. 56, No. 4, 829-839
Published online July 9, 2019
Printed July 31, 2019
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)
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