On a certain functional identity in prime rings. II.
On a certain identitiy satisfied by a derivation and an arbitrary additive mapping. (Summary).
On a certain identity satisfied by a derivation and an arbitrary additive mapping II.
On a certain identity satisfied by a derivation and an arbitrary additive mapping.
On a conjecture of Vukman.
On a generalization of -rings
In this paper rings for which every -torsion quasi-injective module is weakly -divisible for a hereditary preradical are characterized in terms of the properties of the corresponding lattice of the (hereditary) preradicals. In case of a stable torsion theory these rings coincide with -rings investigated by J. Ahsan and E. Enochs in [1]. Our aim was to generalize some results concerning -rings obtained by J.S. Golan and S.R. L’opez-Permouth in [12]. A characterization of the -property in the...
On a problem of Bertram Yood
In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.
On a problem of commutativity of automorphisms.
On -radicals
On a refinement in the classification of the nil rings
On a subset with nilpotent values in a prime ring with derivation
Let be a prime ring, with no non-zero nil right ideal, a non-zero drivation of , a non-zero two-sided ideal of . If, for any , , there exists such that , then is commutative. As a consequence we extend the result to Lie ideals.
On a theorem of J. Vukman.
On Anti-inverse Rings
On anti-inverse rings.
On center-like elements in rings.
On centralizers of semiprime rings
Let be a semiprime ring and an additive mapping such that holds for all . Then is a left centralizer of . It is also proved that Jordan centralizers and centralizers of coincide.
On commutativity of one-sided -unital rings.
On commutativity of rings with constraints on subsets
On dependent elements in rings.
On derivations and commutativity in prime rings.