The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics rank two cluster algebras. These exhibit behavior associated with integrability, namely preservation symplectic form, in tropical case, existence conserved quantity. show certain cases that orbits are unbounded. The related to matrix mutation, from theory able special cases, map is periodi...

Abstract In this paper, we explore a recently emerged approach to the problem of quantisation based on notion ideals. We explicitly prove that nonabelian Volterra together with whole hierarchy its symmetries admits deformation quantisation. show all odd-degree admit also non-deformation discuss for periodic including their quantum Hamiltonians, central elements quantised algebras, and demonstra...

This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between RiemannStieltjes integrals associated with some classes of spectral families including, in particular, those that arise in the context of the Stone representation theorem for Banach spaces is established. The developed approach is applied to the structural analysi...

In this note we provide a topological description of the MacNeille completion of a Heyting algebra similar to the description of the MacNeille completion of a Boolean algebra in terms of regular open sets of its Stone space. We also show that the only varieties of Heyting algebras that are closed under MacNeille completions are the trivial variety, the variety of all Boolean algebras, and the v...

We give an example of a countable theory T such that for every cardinal λ ≥ א2 there is a fully indiscernible set A of power λ such that the principal types are dense over A, yet there is no atomic model of T over A. In particular, T (A) is a theory of size λ where the principal types are dense, yet T (A) has no atomic model. If a complete theory T has an atomic model then the principal types a...

A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks. Mathematics Subject...

Let B(κ, λ) be the subalgebra of P(κ) generated by [κ]. It is shown that if B is any homomorphic image of B(κ, λ) then either |B| < 2 or |B| = |B|, moreover if X is the Stone space of B then either |X| ≤ 2 λ or |X| = |B| = |B|. This implies the existence of 0-dimensional compact T2 spaces whose cardinality and weight spectra omit lots of singular cardinals of “small” cofinality.

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usu...

By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and wecarry out a study on characterization of MV-algebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one non-isomorphic MV-algebra of orders $2$, $3$, $5$ and $7$ and two non-isomorphic MV-algebras of orders $4$ and $6$.