Involve: A Journal of Mathematics
- Volume 12, Number 8 (2019), 1369-1377.
Nonsplit module extensions over the one-sided inverse of $k[x]$
Let be the associative -algebra generated by two elements and with defining relation . A complete description of simple modules over is obtained by using the results of Irving and Gerritzen. We examine the short exact sequence , where and are simple -modules. It shows that nonsplit extension only occurs when both and are one-dimensional, or, under certain condition, is infinite-dimensional and is one-dimensional.
Involve, Volume 12, Number 8 (2019), 1369-1377.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 16D60: Simple and semisimple modules, primitive rings and ideals
Secondary: 16G99: None of the above, but in this section
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