Yasumura, Felipe Yukihide
Published in
Archiv der Mathematik

It was proved by Valenti and Zaicev, in 2011, that if G is an abelian group and K is an algebraically closed field of characteristic zero, then any G-grading on the algebra of upper block triangular matrices over K is isomorphic to a tensor product Mn(K)⊗UT(n1,n2,…,nd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepacka...

Al-Zoubi, Khaldoun Al-Turman, Farah Celikel, Ece Yetkin
Published in
Acta Universitatis Sapientiae, Mathematica

Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of gr-n-ideals of R. We obtain many results concerning gr-n-ideals. Some characterizations of gr-n-ideals and their homogeneous components are given.

Izquierdo, Francisco J Navarro Martín, Antonio J Calderón
Published in
Proceedings - Mathematical Sciences

Let R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {R}$$\end{document} be a ring graded by an arbitrary set A. We show that R\documentclass[12pt]{minimal} \...

Hazrat, Roozbeh Vaš, Lia
Published in
Forum Mathematicum

We consider a generalization K 0 gr ( R ) {K_{0}^{\operatorname{gr}}(R)} of the standard Grothendieck group K 0 ( R ) {K_{0}(R)} of a graded ring R with involution. If Γ is an abelian group, we show that K 0 gr {K_{0}^{\operatorname{gr}}} completely classifies graded ultramatricial * {*} -algebras over a Γ-graded * {*} -field A such that (1) ea...

Wang, Xin Shen, Yuan
Published in
Frontiers of Mathematics in China

We prove an Artin-Schelter regularity result for the method of twisted tensor products under a certain form. Such twisted tensor products, whose twisting maps are determined by the action on the generators, include Ore extensions and double Ore extensions. It is helpful to construct high-dimensional Artin-Schelter regular algebras.

Shen, Y. Wang, X. Zhou, G.-S.
Published in
Results in Mathematics

In this paper, we study the Ext-algebras of graded skew extensions. For a connected graded algebra A and a graded automorphism σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{doc...

Corbet, René Kerber, Michael
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...

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...

Abłamowicz, Rafał
Published in
Advances in Applied Clifford Algebras

Clifford algebras Cℓ2,0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C \ell _{2,0}$$\end{document} and Cℓ1,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepac...

Mao, Xuefeng Gao, Xudong Yang, Yanni Chen, Jiahong
Published in
Science China Mathematics

In this paper, we introduce and study differential graded (DG for short) polynomial algebras. In brief, a DG polynomial algebra A is a connected cochain DG algebra such that its underlying graded algebra A# is a polynomial algebra K[x1,x2,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{...