Mittag-Leffler modules and semi-hereditary rings
Ulrich Albrecht, Alberto Facchini (1996)
Rendiconti del Seminario Matematico della Università di Padova
John Dauns (1992)
Czechoslovak Mathematical Journal
Jacques Raynaud (1984)
Publications du Département de mathématiques (Lyon)
Gary Birkenmeier (1983)
Acta Universitatis Carolinae. Mathematica et Physica
Le Van Thuyet, Phan Dan, Truong Cong Quynh (2016)
Colloquium Mathematicae
We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is -idempotent-invariant if there exists an -envelope u : M → X such that for any idempotent g ∈ End(X) there exists an endomorphism f : M → M such that uf = gu. The properties of this class of modules are discussed. We prove that M is -idempotent-invariant if and only if for every decomposition , we have . Moreover, some generalizations of -idempotent-invariant modules are considered....
Kunio Yamagata (2008)
Colloquium Mathematicae
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.
Ladislav Bican (2008)
Mathematica Bohemica
We shall introduce the class of strongly cancellative multiplicative monoids which contains the class of all totally ordered cancellative monoids and it is contained in the class of all cancellative monoids. If is a strongly cancellative monoid such that for each and if is a ring such that for each , then the class of all non-singular left -modules is a cover class if and only if the class of all non-singular left -modules is a cover class. These two conditions are also equivalent whenever...
Ladislav Bican (2006)
Mathematica Bohemica
Let be a multiplicative monoid. If is a non-singular ring such that the class of all non-singular -modules is a cover class, then the class of all non-singular -modules is a cover class. These two conditions are equivalent whenever is a well-ordered cancellative monoid such that for all elements with there is such that . For a totally ordered cancellative monoid the equalities and hold, being Goldie’s torsion theory.
Ladislav Bican (2006)
Commentationes Mathematicae Universitatis Carolinae
One of the results in my previous paper On torsionfree classes which are not precover classes, preprint, Corollary 3, states that for every hereditary torsion theory for the category -mod with , being Goldie’s torsion theory, the class of all -torsionfree modules forms a (pre)cover class if and only if is of finite type. The purpose of this note is to show that all members of the countable set of rings have the property that the class of all non-singular left modules forms a (pre)cover...
L. Fuchs (1971)
Monatshefte für Mathematik
Paramhans, S.A. (1988)
Portugaliae mathematica
Kalathoor Varadarajan (1992)
Publicacions Matemàtiques
Let X be a class or R-modules containing 0 and closed under isomorphic images. With any such X we associate three classes ΓX, FX and ΔX. The study of some of the closure properties of these classes allows us to obtain characterization of Artinian modules dualizing results of Chatters. The theory of Dual Glodie dimension as developed by the author in some of his earlier work plays a crucial role in the present paper.
Ulrich Albrecht (1990)
Forum mathematicum
Marziyeh Atashkar, Yahya Talebi (2022)
Commentationes Mathematicae Universitatis Carolinae
We introduce the notion of FI-mono-retractable modules which is a generalization of compressible modules. We investigate the properties of such modules. It is shown that the rings over which every cyclic module is FI-mono-retractable are simple Noetherian -ring with zero socle or Artinian semisimple. The last section of the paper is devoted to the endomorphism rings of FI-retractable modules.
Le Duc Thoang, Le Van Thuyet (2006)
Acta Mathematica Universitatis Comenianae. New Series
M. Tamer Koşan, Jan Žemlička (2015)
Colloquium Mathematicae
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.
Andrzej Skowronski (1984)
Acta Universitatis Carolinae. Mathematica et Physica
Khan, Mohd.Z., Zubair, A. (2000)
International Journal of Mathematics and Mathematical Sciences
Dönges, Christoph (1994)
International Journal of Mathematics and Mathematical Sciences
Kent Fuller (1998)
Colloquium Mathematicae