The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a...

We shall make a survey of the most recent results obtained in connection with the programme of investigating notable categorical equivalences for MV-algebras from a topos-theoretic perspective commenced in [3]. In [3] and [2] we generalize to a topos-theoretic setting two classical equivalences arising in the context of MV-algebras: Mundici’s equivalence [4] between the category of MV-algebras ...

The class of finite-dimensional pointed Hopf algebras is a field of current active research. The classification of these algebras has seen substantial progress since the development of the so-called “Lifting method” by Andruskiewitsch and Schneider. With this tool, the case in which the group of group-like elements is abelian is almost completed and recent results by these and other authors suc...

In this paper, we show that the formulæ of Boolean BI cannot distinguish between some of the different notions of separation algebra found in the literature: partial commutative monoids, either cancellative or not, with a single unit or not, all define the same notion of validity. We obtain this result by the careful study of the specific properties of the counter-models that are generated by t...

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After review of κ-Poincaré algebra, illustrate construction classical particle using tools Lie bi-algebras Poisson–Lie groups. We then discuss how construct scalar field theory on non-commutative κ-Minkowski associated group valued nature momenta affects propagation.

This talk is based on [2]. We establish, generalizing Di Nola and Lettieri’s categorical equivalence [3], a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MValgebras. Further, after observing that the two theories are not bi-interpretable in the classical sense, we identify, by considering appropriate topos-theoretic invariants on their common classi...

Let R be the set of real numbers, ⊕ is the maximum operation so that α⊕ β = max{α, β} for any α, β ∈ R. We assume further that Rn ≡ R× . . .×R (n-times, the Cartesian product). We shall solve optimization problems consisting in the minimization of function F (f(x), g(y)), where F : R2 → R1 is an isotone function and function f(x), f : Rn → R1 is defined as follows f(x) = f(x1, . . . , xn) = f1(...

Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...