The transitivity of primary conjugacy in a class of semigroups
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2022-10-25 17:04
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512.53 (66)
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SM ISO690:2012
The transitivity of primary conjugacy in a class of semigroups. In: Quasigroups and Related Systems, 2020, vol. 28, nr. 1(43), pp. 43-46. ISSN 1561-2848.
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Quasigroups and Related Systems
Volumul 28, Numărul 1(43) / 2020 / ISSN 1561-2848

The transitivity of primary conjugacy in a class of semigroups

CZU: 512.53

Pag. 43-46

 
 
 
Disponibil în IBN: 1 iunie 2020


Rezumat

Elements a; b of a semigroup S are said to be primarily conjugate or just p-conjugate, if there exist x; y 2 S1 such that a = xy and b = yx. The p-conjugacy relation generalizes conjugacy in groups, but for general semigroups, it is not transitive. Finding the classes of semigroups in which this notion is transitive is an open problem. The aim of this note is to show that for semigroups satisfying xy 2 fyx; (xy)ng for some n > 1, primary conjugacy is transitive