Published in Forum Mathematicum
We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by Angeleri, Pospíšil, ŠÅ¥ovíček and Trlifaj (2014). We show that the n-tilting classes can equivalently be expressed as classes of all modules vanishing in th...
Published in Algebras and Representation Theory
We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ma...
Published in Mediterranean Journal of Mathematics
We 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 σ[M]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfo...
Published in Analele Universitatii "Ovidius" Constanta - Seria Matematica
In the present work two partial operations in the class of preradicals ℙℝ of the category R-Mod of left R-modules are defined and investigated. They are inverse operations for product with respect to meet and coproduct with respect to join. The criteria of existence of such operations are indicated. Main properties of this operation and relations w...
Published in Journal of Applied and Computational Topology
The Representation Theorem by Zomorodian and Carlsson has been the starting point of the study of persistent homology under the lens of representation theory. In this work, we give a more accurate statement of the original theorem and provide a complete and self-contained proof. Furthermore, we generalize the statement from the case of linear seque...
From Morita theoretic viewpoint, computing Morita invariants is important. We proved that the intersection of the center and the nth socle ZS^{n}(A) :=Z(A)cap mathrm{S}mathrm{o}mathrm{c}^{n}(A) of a finite dimensional algebra A is Morita invariant; This is a generalization of important Morita invariants, the center Z(A) and the Reynolds ideal ZS^{1...
Published in Czechoslovak Mathematical Journal
In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.
Published in Algebras and Representation Theory
A morphism f:M→N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f: M\rightarrow N$\end{document} of left R-modules is called an n-phantom morphism (resp. a Torn-epimorph...
Published in Afrika Matematika
In this paper we introduce the notion of Gabriel topology on semirings as well as on bisemimodules with unities. We also show that there is a lattice isomorphism between the Gabriel topologies on semirings and those on bisemimodules connected via Morita context.
Published in Applied Categorical Structures
We study the transfer of (dual) relative Rickart properties via functors between abelian categories, and we deduce the transfer of (dual) relative Baer property. We also give applications to Grothendieck categories, comodule categories and (graded) module categories, with emphasis on endomorphism rings.
