Gan, Wee Liang Li, Liping
Published in
Selecta Mathematica

We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This implies a linear stable range for the homology of congruence subgroups of general linear groups.

Liu, Yu Zhe Zhang, Chao
Published in
Acta Mathematica Sinica, English Series

An algebra A is called derived-unique provided that any algebra which is derived equivalent to A is necessarily Morita equivalent to A. We classify derived-unique gentle algebras with at most one cycle using the combinatorial invariant introduced by Avella-Alaminos and Geiss.

Zhang, Chao
Published in
Science China Mathematics

Bongartz (2013) and Ringel (2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the finite-dimensional algebras over algebraically closed fields. The present paper mainly studies this "no gaps" theorem as to cohomological length for the bounded derived category Db(A) of a gentle algebra A: if there is an inde...

Gao, Zenghui Peng, Jie
Published in
Czechoslovak Mathematical Journal

Let R be a graded ring and n ⩾ 1 an integer. We introduce and study n-strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that n-strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be m-strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) module...

Itaba, Ayako
Published in
Algebras and Representation Theory

Let k be an algebraically closed field. For a graded algebra, Mori introduced a notion of cogeometric pair (E, σ), where E⊂ℙn−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docu...

Huang, Chonghui Zheng, Lijing
Published in
Open Mathematics

In this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of ExtΛ1(S,Λ) $\begin{array}{} \text{Ext}_{{\it\Lambda}}^{1}(S,\ {\it\Lambda}) \end{array} $ is equal to 1 for any simple Λ-module S with gr S = 1. As a result, we give s...

Chouhy, Sergio Solotar, Andrea
Published in
Algebras and Representation Theory

We solve the isomorphism problem for nonnoetherian down-up algebras A(α, 0, γ) by lifting isomorphisms between some of their noncommutative quotients. The quotients we consider are either quantum polynomial algebras in two variables for γ = 0 or quantum versions of the Weyl algebra A1 for nonzero γ. In particular we obtain that no other down-up alg...

Lukács, Erzsébet Magyar, András
Published in
Czechoslovak Mathematical Journal

Let A be a standard Koszul standardly stratified algebra and X an A-module. The paper investigates conditions which imply that the module Ext* A(X) over the Yoneda extension algebra A* is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar re...

Liang, Li
Published in
Frontiers of Mathematics in China

We investigate stable homology of modules over a commutative noetherian ring R with respect to a semidualzing module C, and give some vanishing results that improve/extend the known results. As a consequence, we show that the balance of the theory forces C to be trivial and R to be Gorenstein.

Di, Zhen Xing Liu, Zhong Kui Zhang, Xiao Xiang
Published in
Acta Mathematica Sinica, English Series

Let R be a right coherent ring and Db(R-Mod) the bounded derived category of left R-modules. Denote by Db(R−Mod)[GF,C]^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${...