## Involve: A Journal of Mathematics

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

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

#### 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.

#### Article information

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

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

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

#### 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

#### References

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