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Short proof of a conjecture concerning split-by-nilpotent extensions

Authors
  • Zito, Stephen
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Springer International Publishing
Publication Date
Jun 19, 2018
Volume
111
Issue
5
Pages
479–483
Identifiers
DOI: 10.1007/s00013-018-1208-7
Source
Springer Nature
Keywords
License
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Abstract

Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E. We provide a short proof to a conjecture by Assem and Zacharia concerning properties of modB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text {mod}}B$$\end{document} inherited by modC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text {mod}}C$$\end{document}. We show if B is a tilted algebra, then C is a tilted algebra.

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