Finitely generated commutative division semirings
Flat semimodules.
Forme algébrique des théories de Stone-Gel'fand
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,...
Full Ideals of Polynomial Rings.
Fully idempotent near-rings and sheaf representations.
Fuzzy congruences on groups and rings.
Fuzzy prime ideals in -rings.
Generalized fuzzy -ideals of semirings with interval-valued membership functions.
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.
Generalized quotients of hemirings
Graph Monoids.
Green’s -relation for the multiplicative reduct of an idempotent semiring
The idempotent semirings for which Green’s -relation on the multiplicative reduct is a congruence relation form a subvariety of the variety of all idempotent semirings. This variety contains the variety consisting of all the idempotent semirings which do not contain a two-element monobisemilattice as a subsemiring. Various characterizations will be given for the idempotent semirings for which the -relation on the multiplicative reduct is the least lattice congruence.
Green's relations in a semiring
-integral near-rings.
Halbringe mit ansteigender Kettenbedingung für Annullatorideale.
Hereditary right Jacobson radical of type- for right near-rings.
Homomorphic images of polynomial near-rings.
Homomorphisms of direct products of algebras