Central extensions in Mal'tsev varieties.
Centrality and normality in protomodular categories.
Characterization of pointed varieties of universal algebras with normal projections.
Characterization of protomodular varieties of universal algebras.
Characterizing tolerance trivial finite algebras
An algebra is tolerance trivial if where is the lattice of all tolerances on . If contains a Mal’cev function compatible with each , then is tolerance trivial. We investigate finite algebras satisfying also the converse statement.
Classes of graphs definable by graph algebra identities or quasi-identities
Closedness properties of internal relations. I. A unified approach to Mal'tsev, unital and subtractive categories.
Closedness properties of internal relations. II: Bourn localization.
Closedness properties of internal relations. IV: Expressing additivity of a category via subtractivity.
Coherence implies congruence-regularity (a local version)
Coherence in varieties of algebras
Commutator theory in strongly protomodular categories.
Compact universal relation in varieties with constants
Completeness theorem for the Evans logic of identities.
Conditions for factorable relations
Conditions for transitive principal tolerances
Congruence classes in regular varieties.
Congruence distributivity in varieties with constants
Congruence restrictions on axes
We give Mal’cev conditions for varieties 4V4 whose congruences on the product , are determined by their restrictions on the axes in .
Congruence submodularity
We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.