-flat and -FP-injective modules
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
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Xiao Yan Yang, Zhongkui Liu (2011)
Czechoslovak Mathematical Journal
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
Mostafa Amini, Driss Bennis, Soumia Mamdouhi (2022)
Czechoslovak Mathematical Journal
Let be a graded ring and be an integer. We introduce and study the notions of Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules by using the notion of special finitely presented graded modules. On -gr-coherent rings, we investigate the relationships between Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules. Among other results, we prove that any graded module in -gr (or gr-) admits a Gorenstein -FP-gr-injective (or Gorenstein -gr-flat) cover and preenvelope, respectively....
Flaviu Pop (2011)
Open Mathematics
In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.
Birkenmeier, Gary F., Groenewald, Nico J. (1999)
Mathematica Pannonica
Günter Pilz, Yong-Sian So (1981)
Monatshefte für Mathematik
Veldsman, Stefan (2001)
Mathematica Pannonica
A. Hanna (1991)
Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry
W.D. Munn (1992)
Semigroup forum
Eva Bayer-Fluckiger, Laura Fainsilber (1996)
Inventiones mathematicae
Elbert M. Pirtle (1986)
Publications de l'Institut Mathématique
Bell, Howard E., Klein, Abraham A. (1999)
International Journal of Mathematics and Mathematical Sciences
Deng Yin Wang, Haishan Pan, Xuansheng Wang (2010)
Czechoslovak Mathematical Journal
Let be an arbitrary parabolic subalgebra of a simple associative -algebra. The ideals of are determined completely; Each ideal of is shown to be generated by one element; Every non-linear invertible map on that preserves ideals is described in an explicit formula.
Robert Gilmer, Matthew O'Malley (1972)
Mathematica Scandinavica
Piotr Dowbor (2001)
Colloquium Mathematicae
Given a group G of k-linear automorphisms of a locally bounded k-category R, the problem of existence and construction of non-orbicular indecomposable R/G-modules is studied. For a suitable finite sequence B of G-atoms with a common stabilizer H, a representation embedding , which yields large families of non-orbicular indecomposable R/G-modules, is constructed (Theorem 3.1). It is proved that if a G-atom B with infinite cyclic stabilizer admits a non-trivial left Kan extension B̃ with the same...
Jan Trlifaj (1991)
Commentationes Mathematicae Universitatis Carolinae
We prove a stronger form, , of a consistency result, , due to Eklof and Shelah. concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that does not hold for left perfect 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...
Michał Jaegermann (1975)
Fundamenta Mathematicae
M.M. Parmenter, P.N. Stewart (1987)
Mathematica Scandinavica
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