A Generalization of Symmetric Inverse Semigroups |
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Authors: | Alexei Vernitski |
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Affiliation: | (1) Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom |
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Abstract: | The set of difunctional binary relations DX plays a special role in representing inverse semigroups by binary relations. However, DX is not an inverse semigroup either with the standard operation ∘, or with an alternative operation introduced in [6]. We introduce a new binary operation ⋄ on the set BX of binary relations. We demonstrate that (DX, ⋄) is an inverse semigroup, and the symmetric inverse semigroup (IX, ∘) is a subsemigroup of (DX,⋄). |
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