Computing the inversion height of some embeddings of the free algebra and the free group algebra

Dolors Herbera; Javier Sánchez

doi:https://doi.org/10.1016/j.jalgebra.2006.11.020

Computing the inversion height of some embeddings of the free algebra and the free group algebra

Dolors Herbera, Javier Sánchez

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

Let X be a set and k a field. We show the so-called JF-embeddings of k 〈 X 〉 in a division ring have inversion height at most two, and give examples of inversion height one and two. We use these embeddings to obtain embeddings of the free group algebra in a division ring of inversion height one and two. © 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	108-131
Journal	Journal of Algebra
Volume	310
DOIs	https://doi.org/10.1016/j.jalgebra.2006.11.020
Publication status	Published - 1 Apr 2007

Keywords

Division ring
Free algebra
Free group algebra
Inversion height
Ore domain

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title = "Computing the inversion height of some embeddings of the free algebra and the free group algebra",

abstract = "Let X be a set and k a field. We show the so-called JF-embeddings of k 〈 X 〉 in a division ring have inversion height at most two, and give examples of inversion height one and two. We use these embeddings to obtain embeddings of the free group algebra in a division ring of inversion height one and two. {\textcopyright} 2006 Elsevier Inc. All rights reserved.",

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author = "Dolors Herbera and Javier S{\'a}nchez",

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AU - Herbera, Dolors

AU - Sánchez, Javier

PY - 2007/4/1

Y1 - 2007/4/1

N2 - Let X be a set and k a field. We show the so-called JF-embeddings of k 〈 X 〉 in a division ring have inversion height at most two, and give examples of inversion height one and two. We use these embeddings to obtain embeddings of the free group algebra in a division ring of inversion height one and two. © 2006 Elsevier Inc. All rights reserved.

AB - Let X be a set and k a field. We show the so-called JF-embeddings of k 〈 X 〉 in a division ring have inversion height at most two, and give examples of inversion height one and two. We use these embeddings to obtain embeddings of the free group algebra in a division ring of inversion height one and two. © 2006 Elsevier Inc. All rights reserved.

KW - Division ring

KW - Free algebra

KW - Free group algebra

KW - Inversion height

KW - Ore domain

U2 - https://doi.org/10.1016/j.jalgebra.2006.11.020

DO - https://doi.org/10.1016/j.jalgebra.2006.11.020

M3 - Article

VL - 310

SP - 108

EP - 131

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -