Remarks on derivations on semiprime rings.
Remarks on generalized derivations in prime and semiprime rings.
Remarks on the structure of the multiplicative monoid of integers modulo m.
Représentation d'anneaux principaux, non nécessairement commutatifs, séparés et complets pour la topologie de Krull
Representing idempotents as a sum of two nilpotents - an approach via matrices over division rings
Right ideals and derivations on multilinear polynomials
Right Utumi p.p.-rings
Rigid left Noetherian rings.
Ring elements as sums of units
In an Artinian ring R every element of R can be expressed as the sum of two units if and only if R/J(R) does not contain a summand isomorphic to the field with two elements. This result is used to describe those finite rings R for which Γ(R) contains a Hamiltonian cycle where Γ(R) is the (simple) graph defined on the elements of R with an edge between vertices r and s if and only if r - s is invertible. It is also shown that for an Artinian ring R the number of connected components of the graph...
Ringe mit nichtkommutativer Addition I.
Ringe mit verallgemeinerter Kupischreihe.
Ringe mit verallgemeinerter Kupischreihe. II.
Rings consisting entirely of certain elements
We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; ; where is a Boolean ring; local ring with nil Jacobson radical; or ; or the ring of a Morita context with zero pairings where the underlying rings are or .
Rings decomposed into direct sums of J-rings and nil rings.
Rings generalized by tripotents and nilpotents
We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).
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 satisfying a certain idempotency condition
Rings with Dense Quasi-Centre.
Rings with many idempotents.