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RISS 인기검색어
- 검색키워드
- 저자 : Yongyan Pu (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
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PULLBACKS OF 𝓒-HEREDITARY DOMAINS
Pu, Yongyan,Tang, Gaohua,Wang, Fanggui Korean Mathematical Society 2018 대한수학회보 Vol.55 No.4
Let (RDTF, M) be a Milnor square. In this paper, it is proved that R is a ${\mathcal{C}}$-hereditary domain if and only if both D and T are ${\mathcal{C}}$-hereditary domains; R is an almost perfect domain if and only if D is a field and T is an almost perfect domain; R is a Matlis domain if and only if T is a Matlis domain. Furthermore, to give a negative answer to Lee, s question, we construct a counter example which is a C-hereditary domain R with $w.gl.dim(R)={\infty}$.
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$w$-Matlis cotorsion modules and $w$-Matlis domains
Yongyan Pu,Gaohua Tang,Fanggui Wang 대한수학회 2019 대한수학회보 Vol.56 No.5
Let $R$ be a domain with its field $Q$ of quotients. An $R$-module $M$ is said to be weak $w$-projective if $\Ext^1_R(M,N)=0$ for all $N\in \mathcal{P}^{\dag}_w$, where $\mathcal{P}^{\dag}_w$ denotes the class of $\GV$-torsionfree $R$-modules $N$ with the property that $\Ext^k_R(M,N)=0$ for all $w$-projective $R$-modules $M$ and for all integers $k\geq 1$. In this paper, we define a domain $R$ to be $w$-Matlis if the weak $w$-projective dimension of the $R$-module $Q$ is $\leq1$. To characterize $w$-Matlis domains, we introduce the concept of $w$-Matlis cotorsion modules and study some basic properties of $w$-Matlis modules. Using these concepts, we show that $R$ is a $w$-Matlis domain if and only if $\Ext^k_R(Q,D)=0$ for any $\mathcal{P}^{\dag}_w$-divisible $R$-module $D$ and any integer $k\geq1$, if and only if every $\mathcal{P}^{\dag}_w$-divisible module is $w$-Matlis cotorsion, if and only if w.$w$-$\pd_RQ/R\leq1$.
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w-MATLIS COTORSION MODULES AND w-MATLIS DOMAINS
Pu, Yongyan,Tang, Gaohua,Wang, Fanggui Korean Mathematical Society 2019 대한수학회보 Vol.56 No.5
Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.
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Pullbacks of $\mathcal{C}$-hereditary domains
Yongyan Pu,Gaohua Tang,Fanggui Wang 대한수학회 2018 대한수학회보 Vol.55 No.4
Let $(RDTF,M)$ be a Milnor square. In this paper, it is proved that $R$ is a $\mathcal{C}$-hereditary domain if and only if both $D$ and $T$ are $\mathcal{C}$-hereditary domains; $R$ is an almost perfect domain if and only if $D$ is a field and $T$ is an almost perfect domain; $R$ is a Matlis domain if and only if $T$ is a Matlis domain. Furthermore, to give a negative answer to Lee$^,$s question, we construct a counter example which is a $\mathcal{C}$-hereditary domain $R$ with $w.gl.\dim(R)=\infty$.
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