Starting with the motivating example of Stone’s representation theorem that allows one to represent Boolean algebras as subalgebras of the poweralgebra of a sufficiently large set, we ask the question of whether it is possible to generalize this to a relationship between lattice theory and topology. This can be done by considering special lattices called locales, which are, in a sense, a suitab...

In this paper a simple algebraic formula is obtained for the correspondence between finite right nilpotent Fp-braces and pre-Lie algebras. This agrees with using Lazard's algebras proposed by Wolfgang Rump in 2014. As an application example, classification of all generated one element cardinality p4 obtained. It also shown that sum number left ideals brace ideal, therefore every contains larges...

In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

where μA (resp. μB) is the multiplication of A (resp. B). We deduce that the ”natural” tensor product μA⊗B = μA ⊗ μB provides A⊗ B with a Lie-admissible algebra structure. In [2] we have defined special classes of Lie-admissible algebras with relations of definition determined by an action of the subgroupsGi of the 3-degree symmetric group Σ3. We obtain quadratic operads, denoted by Gi−Ass and ...

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categ...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...