Weakly $(m,n)$-closed ideals and $(m,n)$-von Neumann regular rings
1
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
Let $R$ be a commutative ring with $ 1 \neq 0$, $I$ a proper ideal of $R$, and $m$ and $n$ positive integers. In this paper, we define $I$ to be a weakly $(m,n)$-closed ideal if $ 0\neq x^{m}\in I$ for $x \in R$ implies $x^{n} \in I$, and $R$ to be an $(m,n)$-von Neumann regular ring if for every $x \in R$, there is an $r \in R$ such that $x^mr = x^n$. A number of results concerning weakly $(m, n)$-closed ideals and $(m,n)$-von Neumann regular rings are given.
Abstract
Let $R$ be a commutative ring with $ 1 \neq 0$, $I$ a proper ideal of $R$, and $m$ and $n$ positive integers. In this paper, we define $I$ to be a weakly $(m,n)$-closed ideal if $ 0\neq x^{m}\in I$ for $x \in R$ implies $x^{n} \in I$, and $R$ to be an $(m,n)$-von Neumann regular ring if for every $x \in R$, there is an $r \in R$ such that $x^mr = x^n$. A number of results concerning weakly $(m, n)$-closed ideals and $(m,n)$-von Neumann regular rings are given.
참고문헌 (15)
- D. D. Anderson, "Weakly prime ideals", Houston J. Math., 29(4), pp.831~840 (2003)
- D. F. Anderson, "On n-absorbing ideals of commutative rings", Comm. Algebra, 39(5), pp.1646~1672 (2011)[DOI]
- D. F. Anderson, "Von Neumann regular and related elements in commutative rings", Algebra Colloq., 19(1), pp.1017~1040 (2012)[DOI]
- D. F. Anderson, "On (m, n)-closed ideals of commutative rings", J. Algebra Appl., 16(1), pp.1750013~ (2017)[DOI]
- A. Badawi, "On 2-absorbing ideals of commutative rings", Bull. Austral. Math. Soc., 75(3), pp.417~429 (2007)[DOI]
- A. Badawi, "On weakly semiprime ideals of commutative rings", Beitr. Algebra Geom., 57(3), pp.589~597 (2016)[DOI]
- A. Badawi, "n-absorbing ideals of commutative rings and recent progress on three conjectures: a survey, in Rings, polynomials, and modules", pp.33~52 (2017), Springer
- A. Badawi, "On weakly 2-absorbing <TEX>${\delta}$<", TEX>-primary ideals in commutative rings, ~
- Ayman Badawi, "On 2-absorbing primary ideals in commutative rings", 대한수학회보, 51(4), pp.1163~1173 (2014), 대한수학회
- Ayman Badawi, "ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS", 대한수학회지, 52(1), pp.97~111 (2015), 대한수학회
- A. Badawi, "On weakly 2-absorbing ideals of commutative rings", Houston J. Math., 39(2), pp.441~452 (2013)
- S. Ebrahimi Atani, "On weakly primary ideals", Georgian Math. J., 12(3), pp.423~429 (2005)
- Brahim Fahid, "$2$-Absorbing $\delta$-primary Ideals in Commutative Rings", Kyungpook Mathematical Journal, 57(2), pp.193~198 (2017), 경북대학교 자연과학대학 수학과
- J. A. Huckaba, "Commutative Rings with Zero Divisors, Monographs and Textbooks in Pure and Applied Mathematics, 117" (1988), Marcel Dekker, Inc.
- H. Mostafanasab, "On weakly n-absorbing ideals of commutative rings", An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 62(2), pp.845~862 (2016)