### Utumi endomorphism rings of dual modules

José L. Gómez Pardo (1989)

Extracta Mathematicae

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José L. Gómez Pardo (1989)

Extracta Mathematicae

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José Gómez Torrecillas, Blas Torrecillas Jover (1991)

Extracta Mathematicae

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Let R be an associative (not necessarily commutative) ring with unit. The study of flat left R-modules permits to achieve homological characterizations for some kinds of rings (regular Von Neumann, hereditary). Colby investigated in [1] the rings with the property that every left R-module is embedded in a flat left R-module and called them left IF rings. These rings include regular and quasi-Frobenius rings. Another useful tool for the study of non-commutative rings is the classical...

Kunio Yamagata (2008)

Colloquium Mathematicae

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We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.

Khazal, R., Dăscălescu, S., Van Wyk, L. (2003)

International Journal of Mathematics and Mathematical Sciences

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Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)

Colloquium Mathematicae

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Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically...

Chen, Weixing (2006)

International Journal of Mathematics and Mathematical Sciences

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Bakkari, Chahrazade, Mahdou, Najib (2009)

Beiträge zur Algebra und Geometrie

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Manfred Dugas, Shalom Feigelstock (2003)

Colloquium Mathematicae

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A ring R is called an E-ring if every endomorphism of R⁺, the additive group of R, is multiplication on the left by an element of R. This is a well known notion in the theory of abelian groups. We want to change the "E" as in endomorphisms to an "A" as in automorphisms: We define a ring to be an A-ring if every automorphism of R⁺ is multiplication on the left by some element of R. We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example...

O. A. S. Karamzadeh, M. Motamedi, S. M. Shahrtash (2004)

Fundamenta Mathematicae

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Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and...

Manfred Dugas, Shalom Feigelstock (2004)

Rendiconti del Seminario Matematico della Università di Padova

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M. Tamer Koşan, Jan Žemlička (2015)

Colloquium Mathematicae

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A module M satisfies the restricted minimum condition if M/N is artinian for every essential submodule N of M. A ring R is called a right RM-ring whenever ${R}_{R}$ satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring R is proved to be an RM-ring if and only if R/Soc(R) is noetherian and every singular module is semiartinian.

Alberto Facchini (1982)

Rendiconti del Seminario Matematico della Università di Padova

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Haily, A., Rahnaoui, H. (2007)

International Journal of Mathematics and Mathematical Sciences

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Cortes, Wagner (2008)

International Journal of Mathematics and Mathematical Sciences

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Lăcrimioara Iancu, Maria S. Pop (2000)

Discussiones Mathematicae - General Algebra and Applications

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We give a construction for (m,n)-rings of quotients of a semicommutative (m,n)-ring, which generalizes the ones given by Crombez and Timm and by Paunić for the commutative case. We also study various constructions involving reduced rings and rings of quotients and give some functorial interpretations.

Eliza Wajch (1988)

Colloquium Mathematicae

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