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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2011, Volume 11, Issue 4, Pages 107–116 (Mi vngu104)  

Groupoids with Primitive Normal and Additive Theories

N. V. Trikashnaya

Institute of Mathematics and Computer Sciences, Far Eastern State University

Abstract: 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, quasigroup.

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English version:
Journal of Mathematical Sciences, 2013, 195:6, 857–864

UDC: 510.8:512.57
Received: 20.04.2011

Citation: N. V. Trikashnaya, “Groupoids with Primitive Normal and Additive Theories”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:4 (2011), 107–116; J. Math. Sci., 195:6 (2013), 857–864

Citation in format AMSBIB
\Bibitem{Tri11}
\by N.~V.~Trikashnaya
\paper Groupoids with Primitive Normal and Additive Theories
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2011
\vol 11
\issue 4
\pages 107--116
\mathnet{http://mi.mathnet.ru/vngu104}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 195
\issue 6
\pages 857--864
\crossref{https://doi.org/10.1007/s10958-013-1624-y}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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