Some characterizations of the commutatorSpringer Science and Business Media LLC - Tập 29 - Trang 61-78 - 1992
A. Day, H. P. Gumm
We start with a characterization of the modular commutator that was given by E. Kiss and the first author in [DK] and explore some of its consequences. Implicit in this characterization is that both the shifting lemma and the cube lemma from [Gu] yield descriptions of the commutator in terms of implications of identities. The shifting lemma translates into the well known term condition and the cub...... hiện toàn bộ
Varieties of abelian topological groups with coproductsSpringer Science and Business Media LLC - Tập 74 - Trang 241-251 - 2015
Saak S. Gabriyelyan, Arkady G. Leiderman, Sidney A. Morris
Varieties of groups, introduced in the 1930s by Garret Birkhoff and B.H. Neumann, are defined as classes of groups satisfying certain laws or equivalently as classes of groups closed under the formation of subgroups, quotient groups, and arbitrary cartesian products. In the 1960s the third author introduced varieties of topological groups as classes of (not necessarily Hausdorff) topological group...... hiện toàn bộ
The variety generated by equivalence algebrasSpringer Science and Business Media LLC - Tập 45 - Trang 211-219 - 2001
J. Ježek, R. McKenzie
Every equivalence relation can be made into a groupoid with the same underlying set if we define the multiplication as follows: xy = x if x,y are related; otherwise, xy = y. The groupoids, obtained in this way, are called equivalence algebras. We find a finite base for the equations of equivalence algebras. The base consists of equations in four variables, and we prove that there is no base consi...... hiện toàn bộ
Equivalence à la Mundici for commutative lattice-ordered monoidsSpringer Science and Business Media LLC - Tập 82 - Trang 1-42 - 2021
Marco Abbadini
We provide a generalization of Mundici’s equivalence between unital Abelian lattice-ordered groups and MV-algebras: the category of unital commutative lattice-ordered monoids is equivalent to the category of MV-monoidal algebras. Roughly speaking, unital commutative lattice-ordered monoids are unital Abelian lattice-ordered groups without the unary operation
...... hiện toàn bộ
Affine completeness of Kleene algebrasSpringer Science and Business Media LLC - Tập 37 - Trang 477-490 - 1997
M. Haviar, K. Kaarli, M. Ploščica
An algebra is called affine complete if all its compatible (i.e. congruence-preserving) functions are polynomial functions. In this paper we characterize affine complete members in the variety of Kleene algebras. We also characterize local polynomial functions of Kleene algebras and use this result to describe locally affine complete Kleene algebras.