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The word problem for nilpotent inverse monoids

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Abstract

The concept ofk-nilpotency is adapted for inverse semigroups andN k(X) is defined as the largestk-nilpotent Rees quotient of the free inverse monoid onX. The membership problem is solved for a certain class of ideals of quasifree inverse monoids. As a consequence, the word problem is shown to be decidable for every finite relation onN k (X), producing an unusual example of total decidability.

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Authors and Affiliations

  1. Departmento de Matemática Faculdade de Ciências, Universidade do Porto, 4000, Porto, Portugal

    Pedro V. Silva

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  1. Pedro V. Silva
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Additional information

Communicated by J. M. Howie

The author acknowledges support from JNICT-Project SAL (PBIC/C/CEN/1021/92) and ESPRIT-BRA Working Group 6317 “ASMICS”.

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Silva, P.V. The word problem for nilpotent inverse monoids. Semigroup Forum 51, 285–293 (1995). https://doi.org/10.1007/BF02573637

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  • DOI: https://doi.org/10.1007/BF02573637

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