Construction of a Nilsemigroup of Paths in a Countable Family of Uniformly Elliptic Complexes

I. A. Ivanov-Pogodaev; A. Ya Kanel-Belov

doi:10.1007/s10469-025-09803-3

Construction of a Nilsemigroup of Paths in a Countable Family of Uniformly Elliptic Complexes

I. A. Ivanov-Pogodaev
, A. Ya Kanel-Belov

Department of Mathematics

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

Abstract

The paper is devoted to the construction of a finitely presented infinite nilsemigroup satisfying the identity x⁹ = 0. We describe an algorithm reducing arbitrary semigroup words to a canonical form. We prove that any word containing a subword of period 9 can be reduced to zero using the defining relations. At the same time, there exist words corresponding to arbitrarily long paths whose length does not decrease, demonstrating that the constructed semigroup is infinite.

Original language	English
Pages (from-to)	410-438
Number of pages	29
Journal	Algebra and Logic
Volume	63
Issue number	6
DOIs	https://doi.org/10.1007/s10469-025-09803-3
State	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to the Siberian Fund of Algebra and Logic 2025.

Keywords

finitely presented groups
finitely presented rings
finitely presented semigroups
nilsemigroups

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10.1007/s10469-025-09803-3

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Construction of a Nilsemigroup of Paths in a Countable Family of Uniformly Elliptic Complexes

Abstract

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Keywords

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