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...
Rings in which ideals are annihilators
Rings radical over P.I. subrings
Rings -radical over -subrings
Rings satisfying a certain idempotency condition
Rings with a finite set of nonnilpotents.
Rings with Radical Maximal Submodules.
Rings without Nilpotent Elements