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ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS
Ayman Badawi,Unsal Tekir,Ece Yetkin 대한수학회 2015 대한수학회지 Vol.52 No.1
Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I or ac ∈ √I or bc ∈ √I. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.
On 2-absorbing primary ideals in commutative rings
Ayman Badawi,Unsal Tekir,Ece Yetkin 대한수학회 2014 대한수학회보 Vol.51 No.4
Let R be a commutative ring with 1 6= 0. In this paper, we introduce the concept of 2-absorbing primary ideal which is a general- ization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ √I or bc ∈ √I. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.
ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS
Badawi, Ayman,Tekir, Unsal,Yetkin, Ece Korean Mathematical Society 2014 대한수학회보 Vol.51 No.4
Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.
ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS
Badawi, Ayman,Tekir, Unsal,Yetkin, Ece Korean Mathematical Society 2015 대한수학회지 Vol.52 No.1
Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, $c{\in}R$ and $0{\neq}abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.
WEAKLY (m, n)-CLOSED IDEALS AND (m, n)-VON NEUMANN REGULAR RINGS
Anderson, David F.,Badawi, Ayman,Fahid, Brahim Korean Mathematical Society 2018 대한수학회지 Vol.55 No.5
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.
Weakly $(m,n)$-closed ideals and $(m,n)$-von Neumann regular rings
David F. Anderson,Ayman Badawi,Brahim Fahid 대한수학회 2018 대한수학회지 Vol.55 No.5
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.