Biregular and uniform identities of algebras
Birkhoff variety theorem for finite algebras
Boolean matrices ... neither Boolean nor matrices
Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Boolean powers as algebras of continuous functions [Book]
Boolean semirings
Bounded countable atomic compactness of ordered groups
Cancellative relations and matrices
Canonical Objects in Classes of (n, V)-Groupoids
AMS Subj. Classification: 03C05, 08B20Free algebras are very important in studying classes of algebras, especially varieties of algebras. Any algebra that belongs to a given variety of algebras can be characterized as a homomorphic image of a free algebra of that variety. Describing free algebras is an important task that can be quite complicated, since there is no general method to resolve this problem. The aim of this work is to investigate classes of groupoids, i.e. algebras with one binary operation,...
Caratterizzazione di una classe di anelli generalizzati
Cardinal and ordinal arithmetics of -ary relational systems and -ary ordered sets
The aim of this paper is to define and study cardinal (direct) and ordinal operations of addition, multiplication, and exponentiation for -ary relational systems. -ary ordered sets are defined as special -ary relational systems by means of properties that seem to suitably generalize reflexivity, antisymmetry, and transitivity from the case of or 3. The class of -ary ordered sets is then closed under the cardinal and ordinal operations.
Cardinal arithmetic of a certain class of monounary algebras
Cardinal arithmetic of general relational systems
Cardinal multiplication of structures with a reflexive relation
Cardinalities of lattices of topologies of unars and some related topics
In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.
Cardinality of retracts of monounary algebras
For an uncountable monounary algebra with cardinality it is proved that has exactly retracts. The case when is countable is also dealt with.
Cartesian closedness in categories of partial algebras.
Categorical equivalences of varieties generated by algebras and
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.
Categories of systems of -relations