Wang, Zhengfang
Published in
Algebras and Representation Theory

Degeneration of modules is defined geometrically. Riedtmann and Zwara show that this degeneration is equivalent to the existence of a certain short exact sequence. Then Yoshino and independently Jensen, Su and Zimmermann generalised this notion to triangulated categories. We write X≤ΔY if X degenerates to Y. In this paper, we prove that ≤△ applied ...

Breaz, Simion Žemlička, Jan
Published in
Algebras and Representation Theory

We will study commuting properties of the defect functor Defß=CokerHomC(ß,-)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\text {Def}_{\beta }=\text {Coker}\text {Hom}...

xu, Dengming
Published in
Archiv der Mathematik

Let M be a finitely generated module over an Artin algebra A. The Auslander–Reiten conjecture says that if ExtAn(M,M⊕A)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$...

Ene, Viviana
Published in
Acta Mathematica Vietnamica

We survey recent results on resolutions of Hibi rings.

Ene, Viviana Herzog, Jürgen Saeedi Madani, Sara
Published in
Manuscripta Mathematica

We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.

Zhan, Jianming Dudek, Wieslaw A. Neggers, J.
Published in
International Journal of Machine Learning and Cybernetics

Molodtsov’s soft set theory provides a general mathematical framework for dealing with uncertainty. The aim of this paper is to lay a foundation for providing a new soft algebraic tool in considering many problems that contain uncertainties. In order to provide these new soft algebraic structures, we introduce the concepts of (M,N)\documentclass[12...

Eisenbud, David Erman, Daniel Schreyer, Frank-Olaf
Published in
Acta Mathematica Vietnamica

We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twists of the sheaf, including, for example, the multigraded module of twisted global sections, and also the Beilinson monads of all twists. Although the Tate resolution is ...

Shi, Hong Bo
Published in
Acta Mathematica Sinica, English Series

The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras — dual and trivially twisted extensions — with a unified combinatorial approach using the two combinatorial algorithms — Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, wit...

Mohammed, Hassen Suleman Esmael Li, Tongtong Chen, Huixiang
Published in
Frontiers of Mathematics in China

We study the Hopf *-algebra structures on the Hopf algebra H(1, q) over ℂ. It is shown that H(1, q) is a Hopf *-algebra if and only if |q| = 1 or q is a real number. Then the Hopf *-algebra structures on H(1, q) are classified up to the equivalence of Hopf *-algebra structures.

Marchesi, Simone Prata, Daniela Moura
Published in
Annali di Matematica Pura ed Applicata (1923 -)

In this work, we will prove results that ensure the simplicity and the exceptionality of vector bundles, which are defined by the splitting of pure resolutions. We will call such objects syzygy bundles.