Dominions, zigzags and epimorphisms for partially ordered semigroups

Nasir Sohail; Lauri Tart

doi:10.12697/ACUTM.2014.18.09

Nasir Sohail Institute of Mathematics, Faculty of Mathematics and Computer Science, University of Tartu, J. Liivi 2, 50409 Tartu
Lauri Tart Institute of Mathematics, Faculty of Mathematics and Computer Science, University of Tartu, J. Liivi 2, 50409 Tartu

DOI: https://doi.org/10.12697/ACUTM.2014.18.09

Keywords: posemigroup, pomonoid, dominion, zigzag, absolutely closed, epimorphism

Abstract

We prove an analogue of Isbell's celebrated zigzag theorem for partially ordered semigroups. This theorem provides a useful description of dominions which we employ to describe absolute closedness of posemigroups and epimorphisms in varieties of absolutely closed posemigroups.

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