Extended Modules and Ore Extensions

Abstract

In this paper, we study extended modules for a special class of Ore extensions. We will assume that R is a ring and A will denote the Ore extension $A:=R[x_1,\ldots ,x_n;\sigma ]$ for which $\sigma $ is an automorphism of R, $x_ix_j=x_jx_i$ and $x_ir=\sigma (r)x_i$, for every $1\le i,j\le n$. 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.

Keywords

Extended modules and rings / Quillen–Suslin’s methods / Ore extensions

References

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Funding

Universidad Nacional de Colombia.(HERMES CODE 26872)