This article is cited in 4 papers

RESEARCH ARTICLE

Generators and relations for the semigroups of increasing functions on $\mathbb N$ and $\mathbb Z$

Vadym Doroshenko

Kyiv Taras Shevchenko University, Department of Mechanics and Mathematics, Volodymyrska, 60, Kyiv 01033, Ukraine

Abstract: The semigroups of all increasing functions over $\mathbb{N}$ and $\mathbb{Z}$ are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semigroups are presented in terms of generators and relations.

Keywords: Order-preserving transformation, monotonic function, generating system, generators and relations, word problem.

MSC: 20M05, 20M20

Received: 13.07.2005
Revised: 28.10.2005

Language: English

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