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arXiv · 1503.02056

Extended modules and Ore extensions

Vyacheslav Artamonov·William Fajardo·Oswaldo Lezama
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Abstract

In this paper we investigate extended modules for a special class of Ore extensions. We will assume that $R$ is a ring and $A$ will denote the Ore extension $A:=R[x_1,\dots,x_n;\sigma]$ for which $\sigma$ is an automorphism of $R$, $x_ix_j=x_jx_i$ and $x_ir=\sigma(r)x_i$, for every $1\leq i,j\leq n$. With some extra conditions over the ring $R$, we will prove Vaserstein's, Quillen's patching, Horrocks' and Quillen-Suslin's theorems for this type of non-commutative rings.

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Vyacheslav Artamonov, William Fajardo, Oswaldo Lezama. 2015-03-06. Extended modules and Ore extensions. https://arxiv.org/abs/1503.02056

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