The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The rst, main, result is that, under reasonable restrictions on the form of the deenition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained c...

This paper begins by introducing the concept of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which is a natural generalization of hom-Lie algebras introduced in a previous paper [14]. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by homomorphisms, twisting the Jacobi identity and skew-symmetry. The nat...

Introduction. The subject matter of this paper belongs to the general theory of sets. The objectives here are the examinations of the structure of classes of sets which are closed under various finite and transfinite set operations and those transformations which preserve these operations. The major results of this paper are partial extensions of (a) the well known theory of cr-algebras (e.g. [...

We present an algebra for data-intensive scalable computing based on monoid homomorphisms that consists of a small set of operations that capture most features supported by current domain-specific languages for data-centric distributed computing. This algebra is being used as the formal basis of MRQL, which is a query processing and optimization system for large-scale distributed data analysis....

We show that the multiplier algebra of the Fourier algebra on a locally compact group G can be isometrically represented on a direct sum on non-commutative L spaces associated to the right von Neumann algebra of G. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful ...

We present a new algebra for complex database objects based on monoids and monoid homomorphisms. The object types supported in our algebra can be any nested composition of collection types, which include lists, sets, multisets, vectors, and matrices. We deene a new calculus equivalent to this algebra, called monoid comprehensions, that captures operations involving diverse collection types in d...

Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of th...