Nil ideals of finite codimension in alternative Noetherian algebras

V. N. Zhelyabin; A. S. Panasenko

doi:10.1134/S0001434617030075

Nil ideals of finite codimension in alternative Noetherian algebras

V. N. Zhelyabin, A. S. Panasenko

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Abstract

Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov’s result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).

Original language	English
Pages (from-to)	460-466
Number of pages	7
Journal	Mathematical Notes
Volume	101
Issue number	3-4
DOIs	https://doi.org/10.1134/S0001434617030075
Publication status	Published - 1 Mar 2017

Keywords

alternative algebra
codimension
exceptional algebra
just infinite algebra
nil ideal
Noetheriaty

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title = "Nil ideals of finite codimension in alternative Noetherian algebras",

abstract = "Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov{\textquoteright}s result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).",

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N2 - Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov’s result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).

AB - Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov’s result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).

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KW - codimension

KW - exceptional algebra

KW - just infinite algebra

KW - nil ideal

KW - Noetheriaty

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Nil ideals of finite codimension in alternative Noetherian algebras

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Keywords

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