Necklace rings and their radicals.
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 -radicals
On radical rings
On the radical theory of involution algebras
On the radical theory of semirings.
On the Radicals of Structural Matrix Rings.
On uniformly strongly prime Γ-semirings (II)
The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.
On unital extensions of near-rings and their radicals.
Prime ideals and strongly prime ideals of skew Laurent polynomial rings.
Radicals Coinciding with the Von Neumann Regular Radical on Artinian Rings.
Radicals induced by the total of rings.
Radicals of semigroup rings of commutative semigroups.
Radicals which coincide on a class of rings.
Radicals which define factorization systems
A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system.
Rad-supplemented modules
Semiprime ideals and irreducible ideals of -semirings.
Skew derivations and the nil and prime radicals
We examine when the nil and prime radicals of an algebra are stable under q-skew σ-derivations. We provide an example which shows that even if q is not a root of 1 or if δ and σ commute in characteristic 0, then the nil and prime radicals need not be δ-stable. However, when certain finiteness conditions are placed on δ or σ, then the nil and prime radicals are δ-stable.
Some graded radicals of graded rings.