Results 21 to 30 of about 607,054 (303)
Semisimple-direct-injective modules
, 2021 The notion of simple-direct-injective modules which are a generalization of injective modules unifies C2 and C3-modules. In the present paper, we introduce the notion of the semisimple-direct-injective module which gives a unified viewpoint of C2, C3 ...
Adel ABYZOV +7 more
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Covers and Envelopes by Submodules or Quotient-Modules
Journal of Mathematics, 2023 Let R be a ring, X a class of left R-modules, S the class of submodules of X, and Q the class of quotient-modules of X. It is shown that SQ is precovering (preenveloping) if and only if every injective (projective) left R-module has an X-precover (X ...
Yuedi Zeng
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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2022 Let 𝑅 be a commutative ring with identity, 𝑀 an 𝑅-module and 𝐸 a torsion-free 𝑅-module. A submodule 𝑁 of 𝑀 is said to be essential (large) in 𝑀 if the intersection of 𝑁 with each nonzero submodule of 𝑀 is nonzero, that is, 𝑁 ∩ 𝑅𝑚 ≠ 0 for any nonzero ...
Osama Naji, Abuzer Gündüz
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On the joint continuity of module multiplication [PDF]
Proceedings of the Estonian Academy of Sciences, 2023 Let A be any topological algebra over R or C. We show that the property of a topological left (right or two-sided) A-module to have a jointly continuous action of A is inherited by submodules, quotient modules, completion, direct products, direct sums ...
Mart Abel
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Localizations of injective modules [PDF]
Proceedings of the Edinburgh Mathematical Society, 1985 The question of whether an injective module E over a noncommutative noetherian ring R remains injective after localization with respect to a denominator set X⊆R is addressed. (For a commutative noetherian ring, the answer is well-known to be positive.) Injectivity of the localization E[X-1] is obtained provided either R is fully bounded (a result of K.
Goodearl, Kenneth R., Jordan, D. A.
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Torsionfree injective modules [PDF]
Pacific Journal of Mathematics, 1969 Abstract not ...
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, 2011 In this paper, we give some characterizations of FP-grinjective R-modules and graded right R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective envelopes and FP-gr-injective covers.
Yang, Xiaoyan, Liu, Zhongkui
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Characterizations of rings and modules by means of lattices [PDF]
, 1965 PhDIn this thesis we study the relationship between the lattice of submodules and the algebraic structure of a module. The key remark in our study will be the fact that the homomorphisms between two independent submadules of a module can be ...
Stephenson, W.
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, 2022 For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for every cyclic right module N. The rings whose simple-injective right modules are injective are exactly the right Artinian rings.
4. Benli-Goral, Sinem +3 more
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On Finitely Annihilated Modules [PDF]
Kirkuk Journal of Science, 2008 Let R be a commutative ring with identity and M be a unitary R-module. An R-module M is called finitely annihilated if there exists a finitely generated R-submodule N of M such that ann(M)=ann(N).Our main purpose in this work is to study this property in
Ali S. Mijbass +2 more
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