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    Vernitski, Alexei 2009. Inverse subsemigroups and classes of finite aperiodic semigroups. Semigroup Forum, Vol. 78, Issue. 3, p. 486.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 129, Issue 3
  • January 1999, pp. 641-647

The finite basis problem for the semigroups of order-preserving mappings

  • A. S. Vernitskii (a1)
  • DOI:
  • Published online: 14 November 2011

Developing an approach of Repnitskii and Volkov, we focus on properties of semigroups of order-preserving mappings on finite chains; in particular, we show that the class of all these semigroups has no finite quasi-identity basis (although it has an infinite one).

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1J. Almeida and M. V. Volkov . The gap between partial and full. Int. J. Algebra Computation 8 (1998), 399430.

2V. A. Gorbunov . Structure of lattices of varieties and lattices of quasivarieties: their similarity and difference. I. Algebra Logika 34 (1995), 142168. (English transl. Algebra Logic 34 (1995), 73–86.)

3V. H. Fernandes . Semigroups of order preserving mappings on a finite chain: a new class of divisors. Semigroup Forum 54 (1997), 230236.

4P. M. Higgins . Divisors of semigroups of order-preserving mappings on a finite chain. Int. J. Algebra Computation 5 (1995), 725742.

5J. E. Pin . Varieties of formal languages (London: North Oxford Academic Publishers, 1986).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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