Extremely noncommutative elements in rings

Howard E. Bell; Abraham A. Klein

doi:10.1007/s00605-007-0505-1

Extremely noncommutative elements in rings

Howard E. Bell^*, Abraham A. Klein

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

We study rings and K-algebras in which all elements or all noncentral elements have smallest possible centralizer. Our principal result asserts that a ring R must be either finite or commutative if each noncentral element a has centralizer equal to the subring generated by a.

Original language	English
Pages (from-to)	19-24
Number of pages	6
Journal	Monatshefte fur Mathematik
Volume	153
Issue number	1
DOIs	https://doi.org/10.1007/s00605-007-0505-1
State	Published - Jan 2008

Keywords

Centralizer
Extremely noncommutative element
Indecomposable ring
Peirce decomposition
Periodic ring
Potent element

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10.1007/s00605-007-0505-1

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title = "Extremely noncommutative elements in rings",

abstract = "We study rings and K-algebras in which all elements or all noncentral elements have smallest possible centralizer. Our principal result asserts that a ring R must be either finite or commutative if each noncentral element a has centralizer equal to the subring generated by a.",

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KW - Extremely noncommutative element

KW - Indecomposable ring

KW - Peirce decomposition

KW - Periodic ring

KW - Potent element

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Extremely noncommutative elements in rings

Abstract

Keywords

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