1,720,982 research outputs found
On Krull-Schmidt finitely accessible categories
No full textLet be a finitely accessible additive category with products, and let be a family of representative classes of finitely presented objects in such that each object is pure-injective. We show that is a Krull-Schmidt category if and only if every pure epimorphic image of the objects is pure-injective
MODULES WHOSE CLOSED SUBMODULES WITH ESSENTIAL SOCLE ARE DIRECT SUMMANDS
No full textWe introduce and study CLESS-modules, which subsume two generalizations of extending modules due to P.F. Smith and A. Tercan. A module M will be called a CLESS-module if every closed submodule N of M (in the sense that M/N is non-singular) with essential socle is a direct summand of M. Various properties concerning direct sums of CLESS-modules are established. We show that, over a Dedekind domain, a module is CLESS if and only if its torsion submodule is a direct summand. We also study the behaviour of CLESS-modules under excellent extensions of rings
Baer-Kaplansky Classes in Grothendieck Categories and Applications
No full textWe study Baer-Kaplansky classes in Grothendieck categories. We apply our results to functor categories, and discuss the transfer of the Baer-Kaplansky property to finitely accessible additive categories, exactly definable additive categories and categories sigma[M]
Transfer of CS-Rickart and dual CS-Rickart properties via functors between Abelian categories
No full textWe study the transfer of (dual) relative CS-Rickart properties via functors between abelian categories. We consider fully faithful functors as well as adjoint pairs of functors. We give several applications to Grothendieck categories and, in particular, to (graded) module and comodule categories
Relatively divisible and relatively flat objects in exact categories: applications
No full textFor a Quillen exact category C endowed with two exact structures D and E such that E subset of D an object X of C is called E-divisible (respectively E-flat) if every short exact sequence from 7, starting (respectively ending) with X belongs to E. We continue our study of relatively divisible and relatively flat objects in Quillen exact categories with applications to finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical
On some radicals and proper classes associated to simple modules
Full text linkFor a unitary right module , there are two known partitions of simple modules in the category : the first one divides them into -injective modules and -small modules, while the second one divides them into -projective modules and -singular modules. We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper classes
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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