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RISS 인기검색어
- 검색키워드
- 저자 : Rahmatinia, Mahdi (검색결과 5 건)
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Darani, Ahmad Yousefian,Rahmatinia, Mahdi Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
The purpose of this paper is to introduce some new class of rings that are closely related to the classes of sharp domains, pseudo-Dededkind domains, TV domains and finite character domains. A ring R is called a ${\phi}$-sharp ring if whenever for nonnil ideals I, A, B of R with $I{\supseteq}AB$, then I = A'B' for nonnil ideals A', B' of R where $A^{\prime}{\supseteq}A$ and $B^{\prime}{\supseteq}B$. We proof that a ${\phi}$-Dedekind ring is a ${\phi}$-sharp ring and we get some properties that by them a ${\phi}$-sharp ring is a ${\phi}$-Dedekind ring.
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Darani, Ahmad Yousefian,Rahmatinia, Mahdi Korean Mathematical Society 2016 대한수학회지 Vol.53 No.5
Let R be a ring in which Nil(R) is a divided prime ideal of R. Then, for a suitable property X of integral domains, we can define a ${\phi}$-X-ring if R/Nil(R) is an X-domain. This device was introduced by Badawi [8] to study rings with zero divisors with a homomorphic image a particular type of domain. We use it to introduce and study a number of concepts such as ${\phi}$-Schreier rings, ${\phi}$-quasi-Schreier rings, ${\phi}$-almost-rings, ${\phi}$-almost-quasi-Schreier rings, ${\phi}$-GCD rings, ${\phi}$-generalized GCD rings and ${\phi}$-almost GCD rings as rings R with Nil(R) a divided prime ideal of R such that R/Nil(R) is a Schreier domain, quasi-Schreier domain, almost domain, almost-quasi-Schreier domain, GCD domain, generalized GCD domain and almost GCD domain, respectively. We study some generalizations of these concepts, in light of generalizations of these concepts in the domain case, as well. Here a domain D is pre-Schreier if for all $x,y,z{\in}D{\backslash}0$, x | yz in D implies that x = rs where r | y and s | z. An integrally closed pre-Schreier domain was initially called a Schreier domain by Cohn in [15] where it was shown that a GCD domain is a Schreier domain.
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Ahmad Yousefian Darani,Mahdi Rahmatinia 대한수학회 2016 대한수학회지 Vol.53 No.5
Let $R$ be a ring in which $Nil(R)$ is a divided prime ideal of $R$. Then, for a suitable property $X$ of integral domains, we can define a $\phi$-$X$-ring if $R/Nil(R)$ is an $X$-domain. This device was introduced by Badawi \cite{Ayman1} to study rings with zero divisors with a homomorphic image a particular type of domain. We use it to introduce and study a number of concepts such as $\phi$-Schreier rings, $\phi$-quasi-Schreier rings, $\phi$-almost-rings, $\phi$-almost-quasi-Schreier rings, $\phi$-$GCD$ rings, $\phi$-generalized $GCD$ rings and $\phi$-almost $GCD$ rings as rings $R$ with $Nil(R)$ a divided prime ideal of $R$ such that $R/Nil(R)$ is a Schreier domain, quasi-Schreier domain, almost domain, almost-quasi-Schreier domain, $GCD$ domain, generalized $GCD$ domain and almost $GCD$ domain, respectively. We study some generalizations of these concepts, in light of generalizations of these concepts in the domain case, as well. Here a domain $D$ is pre-Schreier if for all $x, y, z\in D\backslash 0,$ $x\mid yz$ in $D$ implies that $x=rs$ where $r\mid y$ and $s\mid z$. An integrally closed pre-Schreier domain was initially called a Schreier domain by Cohn in \cite{Cohn} where it was shown that a GCD domain is a Schreier domain.
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DARANI, AHMAD YOUSEFIAN,RAHMATINIA, MAHDI Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.4
This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.
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Some Properties of Dedekind Modules and Q-modules
Motmaen, Shahram,Darani, Ahmad Yousefian,Rahmatinia, Mahdi Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.3
A Q-module is a module in which every nonzero submodule of M is a finite product of primary submodules of M. This paper is devoted to study some properties of Dedekind modules and Q-modules.
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