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Green’s relations in the commutative centralizers of monounary algebras

Jakubíková-Studenovská D., Šuličová M.

Demonstratio Mathematica

2015

Vol. 48, nr 4

536--545

The paper deals with the monounary algebras for which the second centralizer equals the first centralizer. We describe Green’s relations on the semigroup C, where C is the centralizer of such algebra.

On the coset category of a skew lattice

Pita-Costa J.

Demonstratio Mathematica

2014

Vol. 47, nr 3

539--554

Skew lattices are noncommutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper, we will look at the category determined by these rectangular algebras and the morphisms between them, showing that not all skew lattices can determine such a category. Furthermore, we will present a class of examples of skew lattices in rings that are not strictly categorical, and present sufficient conditions for skew lattices of matrices in rings to constitute ^-distributive skew lattices.

Erratum to : On the coset structure of a skew lattice

Pita Costa J.

Demonstratio Mathematica

2013

Vol. 46, nr 2

245--246