On the subgroups of completely decomposable torsion-free groups that are ideals in every ring
In this paper we consider completely decomposable torsion-free groups and we determine the subgroups which are ideals in every ring over such groups.
On torsion-free periodic rings.
Parameterabhängige nichtkommutative Distributionenalgebren
p.p. rings and reduced rings
Primitive idempotents and the socle in group rings of periodic abelian groups
Quelques propriétés des anneaux dont un sous-demi-groupe multiplicatif est un -demi-groupe
Representing idempotents as a sum of two nilpotents - an approach via matrices over division rings
Ringe mit verallgemeinerter Kupischreihe.
Ringe mit verallgemeinerter Kupischreihe. II.
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 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
Semicommutativity of the rings relative to prime radical
In this paper, we introduce a new kind of rings that behave like semicommutative rings, but satisfy yet more known results. This kind of rings is called -semicommutative. We prove that a ring is -semicommutative if and only if is -semicommutative if and only if is -semicommutative. Also, if is -semicommutative, then is -semicommutative. The converse holds provided that is nilpotent and is power serieswise Armendariz. For each positive integer , is -semicommutative if and...
Square subgroups of rank two abelian groups
Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.
Strongly 2-nil-clean rings with involutions
A -ring is strongly 2-nil--clean if every element in is the sum of two projections and a nilpotent that commute. Fundamental properties of such -rings are obtained. We prove that a -ring is strongly 2-nil--clean if and only if for all , is strongly nil--clean, if and only if for any there exists a -tripotent such that is nilpotent and , if and only if is a strongly -clean SN ring, if and only if is abelian, is nil and is -tripotent. Furthermore, we explore the structure...
Strongly regular rings.
Structure of rings with certain conditions on zero divisors.
Sur la décomposition en éléments primaires dans les T-algèbres
Treillis des idempotents centraux d'un anneau