Related papers: Axioms for trimedial quasigroups
We deal with solutions of classical linear equations ax=b and ya=b, applying a particular lattice valued fuzzy technique. Our framework is a structure with a binary operation (a groupoid), equipped with a fuzzy equality. We call it a fuzzy…
We characterize the fuzzy left (resp. right) ideals, the fuzzy ideals and the fuzzy prime (resp. semiprime) ideals of an ordered $\Gamma$-groupoid $M$ in terms of level subsets and we prove that the cartesian product of two fuzzy left…
We consider numerical semigroups associated with normal weighted homogeneous surface singularities with rational homology sphere links. We say that a semigroup is representable if it can be realized in this way. In this article, we study…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
Quasisymmetry builds a third invariant for charged-particle motion besides energy and magnetic moment. We address quasisymmetry at the level of approximate symmetries of first-order guiding-centre motion. We find that the conditions to…
New fundamental mathematical structures are introduced by the triples (left semistructure,right semistructure,bisemistructure) associated with the classical mathematical structures and such that the bisemistructures,resulting from the…
In this work we introduce the notion of almost-symmetry for generalized numerical semigroups. In addition to the main properties occurring in this new class, we present several characterizations for its elements. In particular we show that…
In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode and…
We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.
In this article we give a characterization of left (right) quasi-duo differential polynomial rings. In particular, we show that a differential polynomial ring is left quasi-duo if and only if it is right quasi-duo. This yields a partial…
Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…
In this article, the concept of generalized fuzzy ideals in LA-semigroups. We introduced different types of generalized fuzzy ideals like bi-ideals, interior ideals and quasi ideals in LA-semigroups
We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations…
We present an overview of the theory of self-distributive quasigroups, both in the two-sided and one-sided cases, and relate the older results to the modern theory of quandles, to which self-distributive quasigroups are a special case. Most…
Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a…
In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for…
We consider the pair of degenerate compatible antibrackets satisfying a generalization of the axioms imposed in the triplectic quantization of gauge theories. We show that this actually encodes a Lie group structure, with the antibrackets…
We study C*-algebras associated to right LCM semigroups, that is, semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal. If $P$ is such a…
Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose controlling pair of conformal structures tends…
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…