Rings and modules which are stable under automorphisms of their injective hulls
TLDR
In this article, it was shown that a prime right nonsingular ring R is self-injective if RR is invariant under automorphisms of its injective hull.About:
This article is published in Journal of Algebra.The article was published on 2013-04-01 and is currently open access. It has received 67 citations till now. The article focuses on the topics: Projective module & Injective module.read more
Citations
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Automorphism-invariant modules satisfy the exchange property
TL;DR: In this paper, it was shown that a module invariant under automorphisms of its injective hull satisfies the exchange property and that automorphism-invariant modules are clean.
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Automorphism-invariant modules satisfy the exchange property
TL;DR: In this paper, it was shown that a module invariant under automorphisms of its injective hull satisfies the exchange property and that automorphism-invariant modules are clean.
Journal ArticleDOI
Modules invariant under automorphisms of their covers and envelopes
TL;DR: In this paper, a general theory of modules which are invariant under automorphisms of their covers and envelopes is developed, which is based on several key observations on the additive unit structure of von Neumann regular rings.
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On automorphism-invariant modules
Truong Cong Quynh,M. Tamer Koşan +1 more
TL;DR: The notion of mutually automorphism-invariant modules was introduced in this paper and its connections with pseudo-injective modules are discussed. But the connection between automorphisms of modules and their injective hulls is still open.
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The Schröder–Bernstein problem for modules
TL;DR: In this article, a positive solution for the Schroder-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes, was obtained.
References
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Book
Continuous and Discrete Modules
Saad H. Mohamed,Bruno J. Müller +1 more
TL;DR: Continuous and discrete modules as discussed by the authors are generalizations of infective and projective modules respectively, and they provide an appropriate setting for decomposition theory of von Neumann algebras.
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Modules which are invariant under automorphisms of their injective hulls
Tsiu-Kwen Lee,Yiqiang Zhou +1 more
TL;DR: In this paper, a module is defined to be an automorphism-invariant module if it is invariant under automorphisms of its injective hull, i.e., it is a module that can be regarded as a quasi-injective or injective module.
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Quasi-Injective and Pseudo-Infective Modules
S. K. Jain,Surjeet Singh +1 more
TL;DR: A right R-module is said to be quasi-injective if for every submodule N of M, every R-homomorphism (R-monomorphism) of N into M can be extended to an R-endomorphism of M as mentioned in this paper.
Book
Cyclic Modules and the Structure of Rings
TL;DR: In this paper, the authors consider rings with cyclics @0-injective, q-hypercyclic, pi-hypercycle, and quasi-projective modules.
Related Papers (5)
Modules which are invariant under automorphisms of their injective hulls
Tsiu-Kwen Lee,Yiqiang Zhou +1 more