On the lengths of descendingly flexible and descendingly alternative algebras

A. E. Guterman; S. A. Zhilina

doi:10.1016/j.jalgebra.2024.04.004

On the lengths of descendingly flexible and descendingly alternative algebras

A. E. Guterman, S. A. Zhilina

Department of Mathematics

Bar-Ilan University

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

Abstract

We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field F. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allows us to obtain upper bounds on the lengths of these algebras. We also present an example of an algebra of arbitrarily large dimension such that these bounds are achieved on it asymptotically.

Original language	English
Pages (from-to)	187-220
Number of pages	34
Journal	Journal of Algebra
Volume	651
DOIs	https://doi.org/10.1016/j.jalgebra.2024.04.004
State	Published - 1 Aug 2024

Keywords

Descendingly alternative algebras
Descendingly flexible algebras
Length function

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2024.04.004

Cite this

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abstract = "We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field F. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allows us to obtain upper bounds on the lengths of these algebras. We also present an example of an algebra of arbitrarily large dimension such that these bounds are achieved on it asymptotically.",

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AU - Zhilina, S. A.

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N2 - We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field F. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allows us to obtain upper bounds on the lengths of these algebras. We also present an example of an algebra of arbitrarily large dimension such that these bounds are achieved on it asymptotically.

AB - We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field F. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allows us to obtain upper bounds on the lengths of these algebras. We also present an example of an algebra of arbitrarily large dimension such that these bounds are achieved on it asymptotically.

KW - Descendingly alternative algebras

KW - Descendingly flexible algebras

KW - Length function

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U2 - 10.1016/j.jalgebra.2024.04.004

DO - 10.1016/j.jalgebra.2024.04.004

M3 - مقالة

SN - 0021-8693

VL - 651

SP - 187

EP - 220

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On the lengths of descendingly flexible and descendingly alternative algebras

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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