Cartesian closedness in categories of partial algebras.
Categories of functors between categories with partial morphisms
It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.
Categories of locally diagonal partial algebras.
Closed sets of universal Horn formulas for many-sorted (partial) algebras
Commutation of operations and its relationship with Menger and Mann superpositions
The article considers a problem from Trokhimenko paper [13] concerning the study of abstract properties of commutations of operations and their connection with the Menger and Mann superpositions. Namely, abstract characterizations of some classes of operation algebras, whose signature consists of arbitrary families of commutations of operations, Menger and Mann superpositions and their various connections are found. Some unsolved problems are given at the end of the article.
Completeness theorem for the Evans logic of identities.
Completion varieties
Congruences and ideals in lattice effect algebras as basic algebras
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
Contextual grammars vs. context-free algebras
Convex automorphisms of partial monounary algebras
Convex subsets of partial monounary algebras
Cyclically ordered sets as partial algebras
A representation of cyclically ordered sets by means of partial semigroups with an additional unary operation is constructed.