Semigroup actions on ordered groupoids |
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Authors: | Niovi Kehayopulu Michael Tsingelis |
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Institution: | 1. Department of Mathematics, University of Athens, 15784, Panepistimiopolis Athens, Greece 2. School of Science and Technology Studies in Natural Sciences, Hellenic Open University, Athens, Greece
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Abstract: | In this paper we prove that if S is a commutative semigroup acting on an ordered groupoid G, then there exists a commutative semigroup S? acting on the ordered groupoid G?:=(G × S)/ρ? in such a way that G is embedded in G?. Moreover, we prove that if a commutative semigroup S acts on an ordered groupoid G, and a commutative semigroup S? acts on an ordered groupoid G? in such a way that G is embedded in S?, then the ordered groupoid G? can be also embedded in G?. We denote by ρ? the equivalence relation on G × S which is the intersection of the quasi-order ρ (on G × S) and its inverse ρ ?1. |
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