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RISS 인기검색어
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- 저자 : Gaohua Tang (검색결과 8 건)
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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 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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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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ON φ-VON NEUMANN REGULAR RINGS
Zhao, Wei,Wang, Fanggui,Tang, Gaohua Korean Mathematical Society 2013 대한수학회지 Vol.50 No.1
Let R be a commutative ring with $1{\neq}0$ and let $\mathcal{H}$ = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If $R{\in}\mathcal{H}$, then R is called a ${\phi}$-ring. In this paper, we introduce the concepts of ${\phi}$-torsion modules, ${\phi}$-flat modules, and ${\phi}$-von Neumann regular rings.
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ON COMMUTING GRAPHS OF GROUP RING Z<sub>n</sub>Q<sub>8</sub>
Chen, Jianlong,Gao, Yanyan,Tang, Gaohua Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.1
The commuting graph of an arbitrary ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of group ring $Z_nQ_8$. The main result is that $\Gamma(Z_nQ_8)$ is connected if and only if n is not a prime. If $\Gamma(Z_nQ_8)$ is connected, then diam($Z_nQ_8$)= 3, while $\Gamma(Z_nQ_8)$ is disconnected then every connected component of $\Gamma(Z_nQ_8)$ must be a complete graph with a same size. Further, we obtain the degree of every vertex in $\Gamma(Z_nQ_8)$, the maximum degree and the minimum degree of $\Gamma(Z_nQ_8)$.
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On ø-von Neumann regular rings
Wei Zhao,Fanggui Wang,Gaohua Tang 대한수학회 2013 대한수학회지 Vol.50 No.1
Let R be a commutative ring with 1≠0 and let H={R|R is a commutative ring and Nil(R) is a divided prime ideal}. If R∈H}, then R is called a ø-ring. In this paper, we introduce the concepts of ø-torsion modules, ø-flat modules, and ø-von Neumann regular rings.
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Additive maps of semiprime rings satisfying an Engel condition
Tsiu-Kwen Lee,Yu Li,Gaohua Tang 대한수학회 2021 대한수학회보 Vol.58 No.3
Let $R$ be a semiprime ring with maximal right ring of quotients $Q_{mr}(R)$, and let $n_1, n_2,\ldots ,n_k$ be $k$ fixed positive integers. Suppose that $R$ is $\big(n_1+ n_2+\cdots+n_k\big)!$-torsion free, and that $f\colon \rho\to Q_{mr}(R)$ is an additive map, where $\rho$ is a nonzero right ideal of $R$. It is proved that if $\Big[\big[\ldots [f(x), x^{n_1}],\ldots\big], x^{n_k}\Big]=0$ for all $x\in \rho$, then $\big[f(x), x\big]=0$ for all $x\in \rho$. This gives the result of Beidar et al. \cite{beidar1997} for semiprime rings. Moreover, it is also proved that if $R$ is $p$-torsion, where $p$ is a prime integer with $p=\sum_{i=1}^kn_i$, and if $f\colon R\to Q_{mr}(R)$ is an additive map satisfying $\Big[\big[\ldots [f(x), x^{n_1}],\ldots\big], x^{n_k}\Big]=0$ for all $x\in R$, then $\big[f(x), x\big]=0$ for all $x\in R$.
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