Related papers: Subvarieties of Pseudocomplemented Kleene Algebras
In this paper, we investigate the varieties $\mathbf M_n$ and $\mathbf K_n$ of regular pseudocomplemented de Morgan and Kleene algebras of range $n$, respectively. Priestley duality as it applies to pseudocomplemented de Morgan algebras is…
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…
We present a new construction of a class pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop $A$. Using two injective mappings from one set, $J$, into the second one, $I$, and with an identical copy…
We investigate quasivarieties of (distributive) p-algebras. We sharpen some previous results, give a better picture of the subquasivariety lattice, and prove that quasivarieties generated by free p-algebras belong to a rather small…
The article aims at describing all covers of any finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (concerning their order). Also, all subdirectly irreducible members of…
PBZ*-lattices are bounded lattice-ordered structures endowed with two complements, called Kleene and Brouwer; by definition, they are the paraorthomodular Brouwer-Zadeh lattices in which the pairs of elements with their Kleene complements…
We investigate a construction of a pseudo BL-algebra out of an $\ell$-group called a kite. We show that many well-known examples of algebras related to fuzzy logics can be obtained in that way. We describe subdirectly irreducible kites. As…
Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…
We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting…
We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.
We introduce Kleene-Varlet spaces as partially ordered sets equipped with a polarity satisfying certain additional conditions. By applying Kleene-Varlet spaces, we prove that each regular pseudocomplemented Kleene algebra is isomorphic to a…
The concept of a Kleene algebra (sometimes also called Kleene lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebra. We extend these concepts to posets and show how…
We study the pseudo-Kleene algebras of the Dedekind-MacNeille completion of the ordered set of rough set determined by a reflexive relation. We characterize the cases when PBZ and PBZ*-lattices can be defined on these pseudo-Kleene…
We recall the derived subalgebra of a BCK-algebra, and use this to define the derived ideal. Using the derived ideal, we show that the category of commutative BCK-algebras is a reflective subcategory of the category of BCK-algebras. After…
In this paper, various polynomial representations of strange classical Lie superalgebras are investigated. It turns out that the representations for the algebras of type P are indecomposable, and we obtain the composition series of the…
We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…
The subalgebra of diagonal elements of a quantum matrix group has been conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic algebra, coined the quantum pseudo-plactic algebra. We present a functorial approach to the…
A quasivariety K of algebras has the joint embedding property (JEP) iff it is generated by a single algebra A. It is structurally complete iff the free countably generated algebra in K can serve as A. A consequence of this demand, called…
Pseudo-BCI-algebras generalize both BCI-algebras and pseudo-BCK-algebras, which are a non-commutative generalization of BCK-algebras. In this paper, following [J.G. Raftery and C.J. van Alten, Residuation in commutative ordered monoids with…