共查询到20条相似文献,搜索用时 140 毫秒
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给出了伪投射模的另外一种等价定义,并对伪投射模的自同态环的Jacobson根做了讨论,还对伪投射盖做了某些探讨. 相似文献
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关于内射模和投射模的挠论性质 总被引:6,自引:0,他引:6
设R是有单位元的环.τ表示左R—模范畴中的一个挠理论.本文首先研究了τ—内射模、τ—投射模的有关性质,给出一些等价命题.对QF-环作了刻画,其次讨论了τ—内射模的局部化问题;最后刻画了模的τ—挠根结构及补根.文中有关挠理论的概念见[l]. 相似文献
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杜先能 《数学年刊A辑(中文版)》2006,(2)
本文研究形式三角矩阵环 R 的若干新性质,讨论 R-模的伪投射性,给出了形式三角矩阵环 R 是 V-环或半 V-环的充要条件.同时,给出了 R 是 PS-环的条件. 相似文献
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D. D. Anderson 《代数通讯》2017,45(6):2593-2601
Let M be a left R-module. Then M is a McCoy (resp., dual McCoy) module if for nonzero f(X)∈R[X] and m(X)∈M[X], f(X)m(X) = 0 implies there exists a nonzero r∈R (resp., m∈M) with rm(X) = 0 (resp., f(X)m = 0). We show that for R commutative every R-module is dual McCoy, but give an example of a non-McCoy module. A number of other results concerning (dual) McCoy modules as well as arithmetical, Gaussian, and Armendariz modules are given. 相似文献
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Jaime Castro Pérez Mauricio Medina Bárcenas José Ríos Montes Angel Zaldívar Corichi 《代数通讯》2013,41(11):4749-4768
In this article, we investigate some properties of right core inverses. Particularly, new characterizations and expressions for right core inverses are given, using projections and {1, 3}-inverses. Also, we introduced and investigated a new generalized right core inverse which is called right pseudo core inverse. Then, we provide the relation schema of (one-sided) core inverses, (one-sided) pseudo core inverses, and EP elements. 相似文献
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We determine the multiplicity algebras and multiplicity modules of a p-monomial module. For a general p-group P, we find a sufficient and necessary condition for an endo-monomial P-module to be an endo-permutation P-module, and prove that a capped indecomposable endo-monomial P-module is of p ′-rank. At last, we give an alternative definition of the generalized Dade P-group. 相似文献
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Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). Let F be a fully invariant submodule of M and I?1(F) denotes the set {m∈M:Im?F} for any subset I of S. The module M is called F-Baer if I?1(F) is a direct summand of M for every left ideal I of S. This work is devoted to the investigation of properties of F-Baer modules. We use F-Baer modules to decompose a module into two parts consists of a Baer module and a module determined by fully invariant submodule F, namely, for a module M, we show that M is F-Baer if and only if M = F⊕N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings. 相似文献
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Lixin MAO 《Frontiers of Mathematics in China》2022,17(4):715
We introduce the concept of weak silting modules, which is a generalization of both silting modules and Tor-tilting modules. It is shown that W is a weak silting module if and only if its character module W+ is cosilting. Some properties of weak silting modules are given. 相似文献
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A module M is called a “lifting module” if, any submodule A of M contains a direct summand B of M such that A/B is small in M/B. This is a generalization of projective modules over perfect rings as well as the dual of extending modules. It is well known that an extending module with ascending chain condition (a.c.c.) on the annihilators of its elements is a direct sum of indecomposable modules. If and when a lifting module has such a decomposition is not known in general. In this article, among other results, we prove that a lifting module M is a direct sum of indecomposable modules if (i) rad(M (I)) is small in M (I) for every index set I, or, (ii) M has a.c.c. on the annihilators of (certain) elements, and rad(M) is small in M. 相似文献
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AbstractThe aim of the present paper is to introduce and study the dual concepts of weakly automorphism invariant modules and essential tightness. These notions are non-trivial generalizations of both weakly projectivity, dual automorphism invariant property and cotightness. We obtain certain relations between weakly projective modules, weakly dual automorphism invariant modules and superfluous cotight modules. It is proved that: (1) for right perfect rings, every module is a direct summand of a weakly dual automorphism invariant module and (2) weakly dual automorphism invariant modules are precisely superfluous cotight modules. 相似文献
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