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<p>The paper is devoted to the construction of a finitely presented infinite nilsemigroup satisfying the identity <i>x</i><sup>9</sup> = 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年1月1日

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

摘要

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.