Add to ORKGABSTRACT. It is shown that the adjoint group RŽ of an arbitrary radical ring R has a series with abelian factors and that its finite subgroups are nilpotent. Moreover, some criteria for subgroups of RŽ to be locally nilpotent are given. 1. Introduction. Let R be an associative ring, not necessarily with an identity element. The set of all elements of R is a semigroup with identity element 0 2 R under the operation aŽb = a +b +ab for all a and b in R. The group of all invertible elements of this semigroup is called the adjoint group of R and denoted by RŽ. Following Jacobson [5], a ring R is radical if R = RŽ, which means that R coincides with its Jacobson radical
AbstractLet R = Λ{x1,…, xk} be a p.i. ring, satisfying a monic polynomial identity (one of its coeff...
Several aspects of the theory of radical classes in associative ring theory are investigated. In Ch...
Abstract: In this paper we prove some results on left integral power of Nilpotent radical and Jacobs...
AbstractAn associative ring R, not necessarily with an identity, is called radical if it coincides w...
An associative ring R, not necessarily with an identity, is called radical if it coincides with its ...
AbstractThe set of all elements of an associative ring R, not necessarily with a unit element, forms...
AbstractAn associative ring R without unity is called radical if it coincides with its Jacobson radi...
AbstractThe structure of a periodic radical group G = AB, factorized by two locally nilpotent subgro...
AbstractThis paper contains a number of observations on the semisimplicity problem for group rings w...
AbstractWe study the Jacobson radical of semigroup graded rings. We show that the Jacobson radical o...
summary:For any non-torsion group $G$ with identity $e$, we construct a strongly $G$-graded ring $R$...
We consider some natural relationships between the factors of the central series in groups. It was p...
We study groups in which the non-abelian subgroups fall into finitely many isomorphic classes. We p...
AbstractPerhaps the most interesting and difficult problem in the study of the group ring K[G] is th...
In recent years, Fuchs has described the absolute annihilator and the absolute (Jacobson) radical o...
AbstractLet R = Λ{x1,…, xk} be a p.i. ring, satisfying a monic polynomial identity (one of its coeff...
Several aspects of the theory of radical classes in associative ring theory are investigated. In Ch...
Abstract: In this paper we prove some results on left integral power of Nilpotent radical and Jacobs...
AbstractAn associative ring R, not necessarily with an identity, is called radical if it coincides w...
An associative ring R, not necessarily with an identity, is called radical if it coincides with its ...
AbstractThe set of all elements of an associative ring R, not necessarily with a unit element, forms...
AbstractAn associative ring R without unity is called radical if it coincides with its Jacobson radi...
AbstractThe structure of a periodic radical group G = AB, factorized by two locally nilpotent subgro...
AbstractThis paper contains a number of observations on the semisimplicity problem for group rings w...
AbstractWe study the Jacobson radical of semigroup graded rings. We show that the Jacobson radical o...
summary:For any non-torsion group $G$ with identity $e$, we construct a strongly $G$-graded ring $R$...
We consider some natural relationships between the factors of the central series in groups. It was p...
We study groups in which the non-abelian subgroups fall into finitely many isomorphic classes. We p...
AbstractPerhaps the most interesting and difficult problem in the study of the group ring K[G] is th...
In recent years, Fuchs has described the absolute annihilator and the absolute (Jacobson) radical o...
AbstractLet R = Λ{x1,…, xk} be a p.i. ring, satisfying a monic polynomial identity (one of its coeff...
Several aspects of the theory of radical classes in associative ring theory are investigated. In Ch...
Abstract: In this paper we prove some results on left integral power of Nilpotent radical and Jacobs...