Vol. 12, No. 8, 2019

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Nonsplit module extensions over the one-sided inverse of $k[x]$

Zheping Lu, Linhong Wang and Xingting Wang

Vol. 12 (2019), No. 8, 1369–1377
Abstract

Let R be the associative k-algebra generated by two elements x and y with defining relation yx = 1. A complete description of simple modules over R is obtained by using the results of Irving and Gerritzen. We examine the short exact sequence 0 U E V 0, where U and V are simple R-modules. It shows that nonsplit extension only occurs when both U and V are one-dimensional, or, under certain condition, U is infinite-dimensional and V is one-dimensional.

Keywords
simple modules, representations, module extensions
Mathematical Subject Classification 2010
Primary: 16D60
Secondary: 16G99
Milestones
Received: 8 May 2019
Revised: 8 September 2019
Accepted: 9 September 2019
Published: 25 October 2019

Communicated by Scott T. Chapman
Authors
Zheping Lu
Tandon School of Engineering
New York University
Brooklyn, NY
United States
Linhong Wang
Department of Mathematics
University of Pittsburgh
Pittsburgh, PA
United States
Xingting Wang
Department of Mathematics
Howard University
Washington, DC
United States