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Low Growth Equational Complexity

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posted on 2025-04-01, 04:35 authored by Marcel JacksonMarcel Jackson
The equational complexity function of an equational class of algebras bounds the size of equation required to determine the membership of n-element algebras in. Known examples of finitely generated varieties with unbounded equational complexity have growth in Ω(nc), usually for c ≥ (1/2). We show that much slower growth is possible, exhibiting growth among varieties of semilattice-ordered inverse semigroups and additive idempotent semirings. We also examine a quasivariety analogue of equational complexity, and show that a finite group has polylogarithmic quasi-equational complexity function, bounded if and only if all Sylow subgroups are abelian.

Funding

Complexity in Algebra and Algebra in Complexity: the role of finite semigroups and general algebra

Australian Research Council

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The author was partially supported by the above and Future Fellowship 120100666.

History

Publication Date

2019-01-01

Journal

Proceedings of the Edinburgh Mathematical Society

Volume

62

Issue

1

Pagination

14p. (p. 197-210)

Publisher

Cambridge University Press

ISSN

0013-0915

Rights Statement

© The Author 2018. This article has been published in a revised form in Proceedings of the Edinburgh Mathematical Society https://doi.org/10.1017/S0013091518000354. This version is published under a Creative Commons CC BY-NC-ND licence. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed.

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