Related papers: Relational Algebra as non-Distributive Lattice
We study effectively inseparable (e.i.) pre-lattices (i.e. structures of the form $L=\langle \omega, \wedge, \lor, 0, 1, \leq_L\rangle$ where $\omega$ denotes the set of natural numbers and the following hold: $\wedge, \lor$ are binary…
We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup $\Omega$ (generalization of matching or family associative algebras) or in its cartesian square…
We introduce hybrid algebras as algebraic semantics for hybrid languages with nominals and, possibly, the satisfaction operator. We establish a duality between hybrid algebras and the descriptive two-sorted general frames of Ten Cate. We…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
We try to understand the behavior of exterior algebraic shifting with respect to basic constructions on simplicial complexes, like union and join. In particular we give a complete combinatorial description of the shifting of a disjoint…
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notion…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a…
It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and…
In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative)…
The two-point functions in affine current algebras based on simple Lie algebras are constructed for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
We propose and develop an algebraic approach to revealed preference. Our approach dispenses with non algebraic structure, such as topological assumptions. We provide algebraic axioms of revealed preference that subsume previous, classical…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…