Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2011, Volume 11, Issue 4, Pages 107–116
Groupoids with Primitive Normal and Additive Theories
N. V. Trikashnaya
Institute of Mathematics and Computer Sciences, Far Eastern State University
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.
primitive normal theory, additive theory, semigroup, quasigroup.
PDF file (197 kB)
Journal of Mathematical Sciences, 2013, 195:6, 857–864
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
\paper Groupoids with Primitive Normal and Additive Theories
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\jour J. Math. Sci.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|