weakly prime ideals in commutative semigroups
Bull. Korean Math. Soc.
Published online 2019 Jan 21
D. D. Anderson, Sangmin Chun, and J. R. Juett
Chung-Ang University, Texas State University, The University of Iowa
Abstract : Let S be a commutative semigroup with 0 and 1.
A proper ideal P of S is weakly prime if for a and b in S, nonzero 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
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