Geodesic
On Semigroups Defined by the Identity xxy = y
Publications de l'Institut Mathématique, _N_S_70 (2001) no. 84, p. 1 .

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The groupoid identity $x(xy)=y$ appears in definitions of several classes of groupoids, such as Steiner loops (which are closely related to Steiner triple systems) [9,10], orthogonality in quasigroups [4] and others [12,2]. We have considered in [8] several varieties of groupoids that include this identity among their defining identities, and here we consider the variety ${\mathcal V}$ of semigroups defined by the same identity. The main results are: the decomposition of a ${\mathcal V}$ semigroup as a direct product of a Boolean group and a left unit semigroup; decomposition of the variety ${\mathcal V}$ as a direct product of the variety of Boolean groups and the variety of left unit semigroups; constructions of free objects in ${\mathcal V}$ and the solution of the word problem in ${\mathcal V}$.
Classification : 20M05 20M10
Keywords: semigroup, identity, free object, variety, word problem 
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     title = {On {Semigroups} {Defined} by the {Identity} xxy = y},
     journal = {Publications de l'Institut Math\'ematique},
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     number = {84},
     year = {2001},
     zbl = {1036.20051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_70_84_a0/}
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Smile Markovski; Ana Sokolova; Lidija Goracinova Ilieva. On Semigroups Defined by the Identity xxy = y. Publications de l'Institut Mathématique, _N_S_70 (2001) no. 84, p. 1 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_70_84_a0/