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Extended Modules and Ore Extensions

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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.

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Acknowledgments

Research supported by the project New trends of non-commutative algebra and skew PBW extensions, HERMES CODE 26872, Universidad Nacional de Colombia. The authors are grateful to the editors and the referee for valuable suggestions and corrections.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Viacheslav Artamonov

  2. Universidad Nacional de Colombia, Bogotá, Colombia

    Oswaldo Lezama & William Fajardo

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  1. Viacheslav Artamonov
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  2. Oswaldo Lezama
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  3. William Fajardo
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Correspondence to Viacheslav Artamonov.

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Artamonov, V., Lezama, O. & Fajardo, W. Extended Modules and Ore Extensions. Commun. Math. Stat. 4, 189–202 (2016). https://doi.org/10.1007/s40304-015-0081-y

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  • DOI: https://doi.org/10.1007/s40304-015-0081-y

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