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We introduce hom-Lie-Rinehart algebras as an algebraic analogue of hom-Lie algebroids, and systematically describe a cohomology complex by considering coefficient modules. We define the notion of extensions for hom-Lie-Rinehart algebras. In…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master equations, which can be interpreted as…
Double Boolean algebras (dBas), introduced by Wille, are based on twenty-three identities. We present a simplified axiom system, the D-core algebra, and prove it is equivalent to Wille's original definition. This reduction allows improved…
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…
Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…
We present a way to associate an algebra $B_G (\Upsilon) $ with every pseudo reflection group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized Brauer algebra of simply-laced…
M. Boucetta introduced the notion of pseudo-Riemannian Lie algebra in [2] when he studied the line Poisson structure on the dual of a Lie algebra. In this paper, we redefine pseudo-Riemannian Lie algebra, which, in essence, is a class of…
We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory for periplectic Lie superalgebras. We determine when the algebra is quasi-hereditary and, for fields of characteristic zero, describe the block…
We generalize the Boolean power construction to the setting of compact Hausdorff spaces. This is done by replacing Boolean algebras with de Vries algebras (complete Boolean algebras enriched with proximity) and Stone duality with de Vries…
The a-adic numbers are those groups that arise as Hausdorff completions of noncyclic subgroups of the rational numbers. We give a crossed product construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers and investigate…
Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…
In this paper, we introduce and investigate monadic NM-algebras: a variety of NM-algebras equipped with universal quantifiers. Also, we obtain some conditions under which monadic NM-algebras become monadic Boolean algebras. Besides, we show…
Further to the functional representations of C$^*$-algebras proposed by R. Cirelli, A. Mania and L. Pizzocchero, we consider in this article the uniform K\"ahler bundle (in short, UKB) description of some C$^*$-algebraic subjects. In…
Rook-Brauer algebras are a family of diagram algebras. They contain many interesting subalgebras: rook algebras, Brauer algebras, Motzkin algebras, Temperley-Lieb algebras and symmetric group algebras. In this paper, we generalize the…
We formalise the modal operators from the concurrent dynamic logics of Peleg, Nerode and Wijesekera in a multirelational algebraic language based on relation algebra and power allegories, using relational approximation operators on…
We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality…
Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well known basic propositional logic BL, introduced by H\'ajek, by offering the ability to reason about possibility and necessity of fuzzy…