Utumi endomorphism rings of dual modules
José L. Gómez Pardo (1989)
Extracta Mathematicae
Similarity:
José L. Gómez Pardo (1989)
Extracta Mathematicae
Similarity:
José Gómez Torrecillas, Blas Torrecillas Jover (1991)
Extracta Mathematicae
Similarity:
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
Similarity:
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
Similarity:
Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)
Colloquium Mathematicae
Similarity:
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
Similarity:
Bakkari, Chahrazade, Mahdou, Najib (2009)
Beiträge zur Algebra und Geometrie
Similarity:
Manfred Dugas, Shalom Feigelstock (2003)
Colloquium Mathematicae
Similarity:
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
Similarity:
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
Similarity:
M. Tamer Koşan, Jan Žemlička (2015)
Colloquium Mathematicae
Similarity:
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 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
Similarity:
Haily, A., Rahnaoui, H. (2007)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Cortes, Wagner (2008)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Lăcrimioara Iancu, Maria S. Pop (2000)
Discussiones Mathematicae - General Algebra and Applications
Similarity:
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
Similarity: