Rees Coextensions of Finite Tomonoids and Free Pomonoids

0494908 - ÚI 2020 RIV US eng J - Journal Article
Petrík, Milan - Vetterlein, T.
Rees Coextensions of Finite Tomonoids and Free Pomonoids.
Semigroup Forum. Roč. 99, č. 2 (2019), s. 345-367. ISSN 0037-1912. E-ISSN 1432-2137
R&D Projects: GA ČR GJ15-07724Y
Institutional support: RVO:67985807
Keywords : Totally ordered monoid * Tomonoid * Rees congruence * Rees coextension * Free pomonoid * Finite-valued logic
OECD category: Pure mathematics
Impact factor: 0.448, year: 2019
Method of publishing: Open access

A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We reconsider in this paper the problem of describing the one-element Rees coextensions of a finite, negative tomonoid S, that is, those tomonoids that are by one element larger than S and whose Rees quotient by the poideal consisting of the two smallest elements is isomorphic to S. We show that any such coextension is a quotient of a pomonoid R(S) , called the free one-element Rees coextension of S. We investigate the structure of R(S) and describe the relevant congruences. We moreover introduce a finite family of finite quotients of R(S) from which the coextensions arise in a particularly simple way.
Permanent Link: http://hdl.handle.net/11104/0287953