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arXiv · 1909.08372

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

Zheping Lu·Linhong Wang·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 $0\rightarrow U\rightarrow E \rightarrow V\rightarrow 0$, 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.

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Zheping Lu, Linhong Wang, Xingting Wang. 2019-09-18. Nonsplit module extensions over the one-sided inverse of k[x]. https://arxiv.org/abs/1909.08372

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