Abelizations of weakly associative hyperstructures based on their direct squares
Characteristic of M-polysymmetrical Hyperrings and some properties of M-Polysymmetrical Hyperrings with Unity
Constructions d'hyperanneaux à partir d'anneaux
Directoids with an antitone involution
We investigate -directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids...
El Radical Primo En Sistemas Triples.
F-quasigroups and generalized modules
In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, J. Algebra 317 (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.
F-quasigroups isotopic to groups
In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple FG-quasigroups. Finally,...
Fuzzy congruences on groups and rings.
Fuzzy prime ideals in -rings.
Generalized morphisms of abelian m-ary groups
We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.
Graph Monoids.
Intuitionistic fuzzy -ideals.
L’hyperanneau des classes d’adèles
J’exposerai ici quelques résultats récents (obtenus en collaboration avec C. Consani [3], [4], [5], [6]) qui portent sur le cas limite de la “caractéristique ”. Le but principal est de montrer que l’espace des classes d’adèles d’un corps global, qui jusqu’à présent n’a été considéré que comme un espace (non-commutatif), admet en fait une structure algébrique naturelle. Nous verrons également que la construction de l’anneau de Witt d’un anneau de caractéristique admet un analogue en caractéristique...
Lie ideals in prime Γ-rings with derivations
Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M. In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U)⊂ Z, (ii) d(U)⊂ U and d²(U)=0, (iii) d(U)⊂ U, d²(U)⊂ Z.
Note on isomorphism theorems of hyperrings.
On generalized gamma near-fields.
On injective -modules.
On the Burnside ring and stable cohomotopy of a finite group.
Orthorings
Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.
Ring-like operations is pseudocomplemented semilattices
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.