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. 
@article{VNGU_2011_11_4_a9,
     author = {N. V. Trikashnaya},
     title = {Groupoids with {Primitive} {Normal} and {Additive} {Theories}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {107--116},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_4_a9/}
}
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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/