Reference : Generalized entropy in expanded semigroups and in algebras with neutral element
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Generalized entropy in expanded semigroups and in algebras with neutral element
Lehtonen, Erkko mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Pilitowska, Agata mailto [Warsaw University of Technology > Faculty of Mathematics and Information Science]
Semigroup Forum
Yes (verified by ORBilu)
New York
[en] entropy ; generalized entropy ; neutral element ; associativity ; symmetry ; inverse semigroup ; n-semigroup
[en] The complex product of (non-empty) subalgebras of a given algebra from a variety V is again a subalgebra if and only if the variety V has the so-called generalized entropic property. This paper is devoted to algebras with a neutral element or with a semigroup operation. We investigate relationships between the generalized entropic property and the commutativity of the fundamental operations of the algebra. In particular, we characterize the algebras with a neutral element that have the generalized entropic property. Furthermore, we show that, similarly as for n-monoids and n-groups, for inverse semigroups, the generalized entropic property is equivalent to commutativity.
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