Results 1 to 10 of about 2,745 (167)
A Characterization of Semiprime Rings with Homoderivations
Journal of New Theory, 2023 This paper is focused on the commutativity of the laws of semiprime rings, which satisfy some algebraic identities involving homoderivations on ideals. It provides new and notable results that will interest researchers in this field, such as “R contains ...
Emine Koç Sögütcü
doaj +4 more sources
On the Structure of Semiprime Rings [PDF]
Proceedings of the American Mathematical Society, 1973 The structure of prime rings has recently been studied by A. W. Goldie, R. E. Johnson, L. Lesieur and R. Croisot. In their main results some sort of finiteness assumption is invariably made. It is shown in this paper that certain semiprime rings are subdirect sums of full rings of linear transformations of a right vector space over a division ring.
Augusto H. Ortiz
openalex +2 more sources
On Centrally Semiprime Rings and Centrally Semiprime [PDF]
Kirkuk Journal of Science, 2008 In this paper, two new algebraic structures are introduced which we call a centrally semiprime ring and a centrally semiprime right near-ring, and we look for those conditions which make centrally semiprime rings as commutative rings, so that several ...
Adil Kadir Jabbar +1 more
doaj +2 more sources
Regular elements in semiprime rings [PDF]
Proceedings of the American Mathematical Society, 1968 In the proof of Goldie's theorem [1, Theorem 4.1], one of the crucial steps is to establish that every large right ideal contains a regular element [1, Theorem 3.9]. Recently, S. A. Amitsur told one of the authors he had proved, using the weaker conditions of the ACC on left and right annihilators, that every prime ring contains a left regular element ...
R. E. Johnson, Lawrence S. Levy
+4 more sources
On Centrally Prime and Centrally Semiprime Rings [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2008 In this paper, centrally prime and centrally semiprime rings are defined and the relations between these two rings and prime (resp. semiprime) rings are studied.Among the results of the paper some conditions are given under which prime (resp.
Adil Jabbar, Abdularahman Majeed
doaj +2 more sources
A note on a pair of derivations of semiprime rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are ...
Muhammad Anwar Chaudhry, A. B. Thaheem
doaj +2 more sources
On centralizers of semiprime rings [PDF]
Aequationes Mathematicae, 2003 The main result of this paper is the following. Let R be a 2-torsion free semiprime ring and let $ T : R \rightarrow R $ be an additive mapping such that $ 2T(xyx) = T(x)yx + xyT(x) $ holds for all $ x,y \in R $. Then T is a centralizer.
Joso Vukman, Irena Kosi-Ulbl
openalex +3 more sources
DERIVATIONS OF PRIME AND SEMIPRIME RINGS [PDF]
Journal of the Korean Mathematical Society, 2009 Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x)) n = xy + yx for all x,y 2 I, then R is commutative. (ii) If charR 6 2 and (d(x)y + xd(y) + d(y)x + yd(x)) n i (xy + yx) is central for all x,y 2 I, then R is commutative.
Nurcan Argaç, Hülya İnceboz
openalex +5 more sources
A note on derivations in semiprime rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 We prove in this note the following result. Let n>1 be an integer and let R be an n!-torsion-free semiprime ring with identity element. Suppose that there exists an additive mapping D:R→R such that D(xn)=∑j=1nxn−jD(x)xj−1 is fulfilled for all x∈R.
Joso Vukman, Irena Kosi-Ulbl
doaj +2 more sources
On Semiprime Rings of Bounded Index [PDF]
Proceedings of the American Mathematical Society, 1982 A ring R R is of bounded index (of nilpotency) if there is an integer n ⩾ 1 n \geqslant 1 such that x n = 0 {x^n} = 0 whenever x ∈ R x \in R is nilpotent. The least
Efraim P. Armendariz
openalex +3 more sources