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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.
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참고문헌 (4)
참고문헌 신청
D. D. Anderson / 1984 / Ideal theory in commutative semigroups / Semigroup Forum 30(1):127~158
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29(4):831~840
D. D. Anderson / 1996 / Factorization in commutative rings with zero divi-sors / Rocky Mountain J. Math 26(2):439~480
Yasuyuki Hirano / 2010 / ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME / 대한수학회보 47(5):1077~1087
D. D. Anderson / 2003 / Weakly prime ideals / Houston J. Math 29(4):831~840
D. D. Anderson / 1996 / Factorization in commutative rings with zero divi-sors / Rocky Mountain J. Math 26(2):439~480
Yasuyuki Hirano / 2010 / ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME / 대한수학회보 47(5):1077~1087
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