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A Generalization of Symmetric Inverse Semigroups

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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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  1. Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom

    Alexei Vernitski

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  1. Alexei Vernitski
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Correspondence to Alexei Vernitski.

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Vernitski, A. A Generalization of Symmetric Inverse Semigroups. Semigroup Forum 75, 417–426 (2007). https://doi.org/10.1007/s00233-007-0710-1

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  • DOI: https://doi.org/10.1007/s00233-007-0710-1

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