|
Fundamentalnaya i Prikladnaya Matematika, 2009, Volume 15, Issue 7, Pages 165–177
(Mi fpm1276)
|
|
|
|
This article is cited in 6 scientific papers (total in 6 papers)
Abelian and Hamiltonian groupoids
A. A. Stepanova, N. V. Trikashnaya Far Eastern National University
Abstract:
In this work, we investigate some groupoids that are Abelian algebras and Hamiltonian algebras. An algebra is Abelian if for every polynomial operation and for all elements $a,b,\bar c,\bar d$ the implication $t(a,\bar c)=t(a,\bar d)\Longrightarrow t(b,\bar c)=t(b,\bar d)$ holds. An algebra is Hamiltonian if every subalgebra is a block of some congruence on the algebra. R. J. Warne in 1994 described the structure of the Abelian semigroups. In this work, we describe the Abelian groupoids with identity, the Abelian finite quasigroups, and the Abelian semigroups $S$ such that $abS=aS$ and $Sba=Sa$ for all $a,b\in S$. We prove that a finite Abelian quasigroup is a Hamiltonian algebra. We characterize the Hamiltonian groupoids with identity and semigroups under the condition of Abelianity of these algebras.
Citation:
A. A. Stepanova, N. V. Trikashnaya, “Abelian and Hamiltonian groupoids”, Fundam. Prikl. Mat., 15:7 (2009), 165–177; J. Math. Sci., 169:5 (2010), 671–679
Linking options:
https://www.mathnet.ru/eng/fpm1276 https://www.mathnet.ru/eng/fpm/v15/i7/p165
|
Statistics & downloads: |
Abstract page: | 362 | Full-text PDF : | 158 | References: | 51 | First page: | 1 |
|