Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 8 (2019), 1369-1377.

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

Zheping Lu, Linhong Wang, and Xingting Wang

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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 0UEV0, 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.

Article information

Source
Involve, Volume 12, Number 8 (2019), 1369-1377.

Dates
Received: 8 May 2019
Revised: 8 September 2019
Accepted: 9 September 2019
First available in Project Euclid: 12 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.involve/1576119632

Digital Object Identifier
doi:10.2140/involve.2019.12.1369

Mathematical Reviews number (MathSciNet)
MR4041270

Zentralblatt MATH identifier
07162471

Subjects
Primary: 16D60: Simple and semisimple modules, primitive rings and ideals
Secondary: 16G99: None of the above, but in this section

Keywords
simple modules representations module extensions

Citation

Lu, Zheping; Wang, Linhong; Wang, Xingting. Nonsplit module extensions over the one-sided inverse of $k[x]$. Involve 12 (2019), no. 8, 1369--1377. doi:10.2140/involve.2019.12.1369. https://projecteuclid.org/euclid.involve/1576119632


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References

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