Radicals of Regular Near Rings.
Radicals of semigroup rings of commutative semigroups.
Radicals of semigroup rings of orthogroups.
Radicals of symmetric cellular algebras
For a symmetric cellular algebra, we study properties of the dual basis of a cellular basis first. Then a nilpotent ideal is constructed. The ideal connects the radicals of cell modules with the radical of the algebra. It also yields some information on the dimensions of simple modules. As a by-product, we obtain some equivalent conditions for a finite-dimensional symmetric cellular algebra to be semisimple.
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.
Radikale von separablen Algebren über Ringen.
Rad-supplemented modules
Range inclusion results for derivations on noncommutative Banach algebras
Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...
Regular generalized adjoint semigroups of a ring.
Regular Rings and Baer Rings.
Remarks on derivations on semiprime rings.
Remarks on generalized derivations in prime and semiprime rings.
Representing idempotents as a sum of two nilpotents - an approach via matrices over division rings
Right ideals and derivations on multilinear polynomials
Right Sided Ideals and Multilinear Polynomials with Derivation on Prime Rings
Ringe mit verallgemeinerter Kupischreihe.
Rings decomposed into direct sums of J-rings and nil rings.
Rings in which elements are sum of a central element and an element in the Jacobson radical
An element in a ring is called CJ if it is of the form , where belongs to the center and is an element from the Jacobson radical. A ring is called CJ if each element of is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show that the...
Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute
An element in a ring R with identity is said to be strongly nil clean if it is the sum of an idempotent and a nilpotent that commute, R is said to be strongly nil clean if every element of R is strongly nil clean. Let C(R) be the center of a ring R and g(x) be a fixed polynomial in C(R)[x]. Then R is said to be strongly g(x)-nil clean if every element in R is a sum of a nilpotent and a root of g(x) that commute. In this paper, we give some relations between strongly nil clean rings and strongly...