An analogue of the Magnus problem for associative algebras

Natalia Iyudu; V. Dotsenko; D. Korytin

doi:10.1007/s10958-005-0457-8

An analogue of the Magnus problem for associative algebras

Natalia Iyudu
, V. Dotsenko
, D. Korytin

School of Mathematics and Physics

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

1 Citation (Scopus)

Abstract

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

Original language	English
Pages (from-to)	6023-6026
Number of pages	4
Journal	Journal of Mathematical Sciences
Volume	131
Issue number	6
DOIs	https://doi.org/10.1007/s10958-005-0457-8
Publication status	Published - Dec 2005

ASJC Scopus subject areas

General Mathematics

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title = "An analogue of the Magnus problem for associative algebras",

abstract = "We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by \$n+k\$ generators and \$k\$ relations and has an \$n\$-element system of generators, then this algebra is a free algebra of rank \$n\$.",

author = "Natalia Iyudu and V. Dotsenko and D. Korytin",

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T1 - An analogue of the Magnus problem for associative algebras

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AU - Dotsenko, V.

AU - Korytin, D.

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Y1 - 2005/12

N2 - We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

AB - We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

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DO - 10.1007/s10958-005-0457-8

M3 - Article

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SP - 6023

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JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 6

ER -

An analogue of the Magnus problem for associative algebras

Abstract

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