논문KCI 등재
Weakly prime ideals in commutative semigroups
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
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.
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.
참고문헌 (4)
- D. D. Anderson, "Ideal theory in commutative semigroups", Semigroup Forum, 30(1), pp.127~158 (1984), Springer Science and Business Media LLC[DOI]
- D. D. Anderson, "Weakly prime ideals", Houston J. Math, 29(4), pp.831~840 (2003)
- D. D. Anderson, "Factorization in commutative rings with zero divi-sors", Rocky Mountain J. Math, 26(2), pp.439~480 (1996)[DOI]
- Yasuyuki Hirano, "ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME", 대한수학회보, 47(5), pp.1077~1087 (2010), 대한수학회
관련 논문AI추천
On 2-absorbing Primary Ideals of Commutative SemigroupBiswaranjan Khanra, Manasi Mandal경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제3호On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative SemiringsAhmad Yousefian Darani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제1호Pure Ideals in Ordered SemigroupsJatuporn Sanborisoot, Thawhat Changphas경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호Weakly prime left ideals in near-subtraction semigroupsG. Satheesh Kumar, P. Dheena대한수학회 · 대한수학회논문집2008 · 제23권 제3호On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative SemiringFatemeh Soheilnia경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호Zero-divisors of Semigroup ModulesPeyman Nasehpour경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2011 · 제51권 제1호
이 간행물의 다른 논문 (17건)
On the denominator of Dedekind sumsSt'ephane R. Louboutinpp. 815-827Generalized Myers theorem for Finsler manifolds with integral Ricci curvature boundBing-Ye Wupp. 841-852Gradient estimates of a nonlinear elliptic equation for the $V$-LaplacianFanqi Zengpp. 853-865Geometric characterizations of canal surfaces in Minkowski 3-space $\mathbb{I}$Mengfei Su, 부설산, Jinhua Qian, 정승달pp. 867-883A note on the first order commutator $\mathcal{C}_2$Wenjuan Li, Suying Liupp. 885-898