Related papers: Rough sets and three-valued structures
The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…
Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three…
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
A new class of noncommutative $k$-algebras (for $k$ an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first order theory is assigned describing models of a…
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
In this note research and publications by Zdzis{\l}aw Pawlak and his collaborators from 1970s and 1981 are recalled. Focus is placed on the sources of inspiration which one can identify on the basis of those publications. Finally,…
Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this paper, we re-study the correspondence between…
Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are…
This is a survey on formality results relying on weight structures. A weight structure is a naturally occurring grading on certain differential graded algebras. If this weight satisfies a purity property, one can deduce formality. Algebraic…
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…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
We construct and study SUSY lattice vertex algebras. As a simple example, we obtain the simple vertex algebra associated to the vertex algebra $V_c(N3)$ of central charge $c=3/2$, as the SUSY lattice vertex algebra associated to…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $\Omega(|A|^{3/2})$ three-term arithmetic progressions.
The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik's double affine Hecke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin…
We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.