Geodesic
Groupoids with Primitive Normal and Additive Theories
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 4, pp. 107-116

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In this work we investigate some groupoids with primitive normal and additive theories. We prove that the theory of a semigroup is primitive normal iff this semigroup is an inflation of rectangular band of the abelian groups and the product of its idempotents is an idempotent; the theory of semigroups is additive iff this semigroup is an abelian group. We show that for the theory of a finite quasigroup the notions of primitive normality, additivity and abelianty are equivalent. We prove that the theory of a groupoid with an identity is primitive normal iff this theory is additive, which is equivalent to a groupoid to be an abelian group.
Keywords: primitive normal theory, additive theory, semigroup
Mots-clés : quasigroup. 
N. V. Trikashnaya. Groupoids with Primitive Normal and Additive Theories. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 4, pp. 107-116. http://geodesic.mathdoc.fr/item/VNGU_2011_11_4_a9/
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