Results 121 to 130 of about 1,324,184 (168)

Semiprime Rings with Nilpotent Derivatives

Canadian Mathematical Bulletin, 1981
There has been a great deal of work recently concerning the relationship between the commutativity of a ring JR and the existence of certain specified derivations of R. Bell, Herstein, Procesei, Schacher, Ligh, Martindale, Putcha, Wilson, and Yaqub [1, 2, 6, 8, 9, 10, 11, 12, 14] have studied conditions on commutators which imply the commutativity of ...
Chung, L. O., Luh, Jiang
openaire   +1 more source

On commuting additive mappings on semiprime rings

, 2020
The main purpose of this paper is to describe the structure of a pair of additive mappings that are commuting on a semiprime ring.
Siriporn Lapuangkham, U. Leerawat
semanticscholar   +1 more source

Centralizing Mappings of Semiprime Rings

Canadian Mathematical Bulletin, 1987
AbstractLet R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal.
Bell, H. E., Martindale, W. S. III
openaire   +2 more sources

Action of higher derivations on semiprime rings

Georgian Mathematical Journal
Let m , n {m,n} be the fixed positive integers and let ℛ {\mathcal{R}} be a ring. In 1978, Herstein proved that a 2-torsion free prime ring ℛ {\mathcal{R}} is commutative if there is a nonzero derivation d of R such that [ d ⁢ ( ϱ ) , d ⁢ ( ξ ) ] = 0 {[d(
Shakir Ali, Vaishali Varshney
semanticscholar   +1 more source

THE SOURCE OF SEMIPRIMENESS OF RINGS

2018
Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar ...
Aydin, Neset, Demir, Cagri, Camci, Didem Karalarlioglu   +2 more
openaire   +2 more sources

On the Adjoint Group of Semiprime Rings

Communications in Algebra, 2006
An associative ring R, not necessarily with a unity, is called semiprime if it has no nonzero nilpotent ideal. It is proved that in the adjoint group of a semiprime ring R every soluble-by-finite normal subgroup centralizes the Jacobson radical of R. In particular, if R is a semiprime ring with unity, then the same result holds for the multiplicative ...
CATINO, Francesco, MICCOLI, Maria Maddalena, Y.a. P. SYSAK   +2 more
openaire   +2 more sources

On Prime and Semiprime Rings with Derivations

Algebra Colloquium, 2006
Let R be a ring and S a nonempty subset of R. A mapping f: R → R is called commuting on S if [f(x),x] = 0 for all x ∈ S. In this paper, firstly, we generalize the well-known result of Posner related to commuting derivations on prime rings. Secondly, we show that if R is a semiprime ring and I is a nonzero ideal of R, then a derivation d of R is ...
openaire   +3 more sources

A note on inner and reflexive inverses in semiprime rings

Journal of Algebra and its Applications, 2020
Let [Formula: see text] be a semiprime ring, not necessarily with unity, and [Formula: see text]. Let [Formula: see text] (respectively, [Formula: see text]) denote the set of inner (respectively, reflexive) inverses of [Formula: see text] in [Formula ...
Tsiu-Kwen Lee
semanticscholar   +1 more source

Semiprime Rings with Hypercentral Derivations

Canadian Mathematical Bulletin, 1995
AbstractLetRbe a semiprime ring with a derivationd, λ a left ideal ofRandk, ntwo positive integers. Suppose that[d(xn),xn]k= 0 for allx∊ λ. Then [λ,R]d(R)= 0. That is, there exists a central idempotente∊U, the left Utumi quotient ring ofR, such thatdvanishes identically oneUand λ(l —e) is central in (1 —e ...
openaire   +2 more sources

On Jordan Structure in Semiprime Rings

Canadian Journal of Mathematics, 1976
A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and
openaire   +1 more source