On injectivity, p-injectivity and YJ-injectivity.
On intecomposable Lattices over Twisted group rings
On Interassociativity and Related Questions
On involution rings with unique minimal *-subring.
On isomorphic commutative group algebras of Abelian groups with -projective quotients.
On Jacobson radical of a -semiring.
On Jordan ideals and derivations in rings with involution
Let be a -torsion free -prime ring, a derivation which commutes with and a -Jordan ideal and a subring of . In this paper, it is shown that if either acts as a homomorphism or as an anti-homomorphism on , then or . Furthermore, an example is given to demonstrate that the -primeness hypothesis is not superfluous.
On Jordan ideals and left -derivations in prime rings.
On -ideals of semirings.
On K2 of Finite Dimensional Division Algebras Over Arithmetical Fields.
On Kolchin's theorem.
A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent.Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite dimensional algebra...
On k-radicals of Green's relations in semirings with a semilattice additive reduct
We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.
On Krull dimension of Ore extensions.
On -fuzzy ideals in semirings. I
In this paper we extend the concept of an -fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring , and we show that each level left (resp. right) ideal of an -fuzzy left (resp. right) ideal of is characteristic iff is -fuzzy characteristic.
On -fuzzy ideals in semirings. II
We study some properties of -fuzzy left (right) ideals of a semiring related to level left (right) ideals.
On large selforthogonal modules
We construct non faithful direct summands of tilting (resp. cotilting) modules large enough to inherit a functorial tilting (resp. cotilting) behaviour.
On left, right and two-sided cancellable elements of semigroups.
On left -derivations of prime rings
Let be a -torsion free prime ring. Suppose that are automorphisms of . In the present paper it is established that if admits a nonzero Jordan left -derivation, then is commutative. Further, as an application of this resul it is shown that every Jordan left -derivation on is a left -derivation on . Finally, in case of an arbitrary prime ring it is proved that if admits a left -derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal of , then ...
On L-ideal-based L-zero-divisor graphs
In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.
On Lie algebras in braided categories
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...