General algebraic geometry and formal concept analysis.
Generalized deductive systems in subregular varieties
An algebra is subregular alias regular with respect to a unary term function if for each we have whenever for each . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset is a class of some congruence on containing if and only if is this generalized deductive system. This method is efficient (needs a finite number of steps).
Generalized ordering and partitions
Graphical Compositions and Weak Congruences
Green's relations and their generalizations on semigroups
Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups.
Group congruences on eventually inverse semigroups
Group congruences on regular semigroups.