Inverse semigroups with apartness
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The notion of semigroups with apartness has been introduced recently as a constructive counterpart of classical semigroups. On such structures, a constructive analogue of the isomorphism theorem has been proved, and quasiorder relations and related substructures have been studied. In this paper, we extend this approach by introducing inverse semigroups with apartness, a useful tool to describe partial symmetries in sets with apartness. We prove a constructive analogue of the isomorphism theorem for inverse semigroups and provide a characterisation of cocongruences on inverse semigroups.
KeywordsSet with apartness Semigroup with apartness Inverse semigroup with apartness Cocongruence
The authors acknowledge the research cooperation project among Department of Mathematics of Politecnico di Milano, Faculty of Science of the University of Novi Sad, and the Department of Mathematics and Computer Science of the University of Maribor. In this framework, Professor Crvenković gave a talk on semigroups with apartness which drew our attention to constructive algebra. The authors thank the referee for constructive comments and recommendations which helped to improve the readability and quality of the paper.
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