A note on multiplicative commutators of division rings

Roozbeh Hazrat

doi:10.1142/S0219498819500312

A note on multiplicative commutators of division rings

Roozbeh Hazrat

Western Sydney University

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

2 Citations (Scopus)

Abstract

We give an example of a division ring D whose multiplicative commutator subgroup does not generate D as a vector space over its center, thus disproving the conjecture posed in [M. Aghabali, S. Akbari, M. Ariannejad and A. Madadi, Vector space generated by the multiplicative commutators of a division ring, J. Algebra Appl.12(8) (2013) 7 pp.].

Original language	English
Article number	1950031
Number of pages	2
Journal	Journal of Algebra and Its Application
Volume	18
Issue number	2
DOIs	https://doi.org/10.1142/S0219498819500312
Publication status	Published - 2019

Keywords

algebra
division rings

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10.1142/S0219498819500312

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abstract = "We give an example of a division ring D whose multiplicative commutator subgroup does not generate D as a vector space over its center, thus disproving the conjecture posed in [M. Aghabali, S. Akbari, M. Ariannejad and A. Madadi, Vector space generated by the multiplicative commutators of a division ring, J. Algebra Appl.12(8) (2013) 7 pp.].",

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AU - Hazrat, Roozbeh

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AB - We give an example of a division ring D whose multiplicative commutator subgroup does not generate D as a vector space over its center, thus disproving the conjecture posed in [M. Aghabali, S. Akbari, M. Ariannejad and A. Madadi, Vector space generated by the multiplicative commutators of a division ring, J. Algebra Appl.12(8) (2013) 7 pp.].

KW - algebra

KW - division rings

UR - https://hdl.handle.net/1959.7/uws:54500

U2 - 10.1142/S0219498819500312

DO - 10.1142/S0219498819500312

M3 - Article

SN - 0219-4988

VL - 18

JO - Journal of Algebra and Its Application

JF - Journal of Algebra and Its Application

IS - 2

M1 - 1950031

ER -

A note on multiplicative commutators of division rings

Abstract

Keywords

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