Results 41 to 50 of about 2,393 (148)
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 ...
Johnson, R. E., Levy, L. S.
openaire +2 more sources
Identities on additive mappings in semiprime rings
Математичні Студії, 2023 Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation ...
A. Z. Ansari, N. Rehman
doaj +1 more source
ON JORDAN IDEAL IN PRIME AND SEMIPRIME INVERSE SEMIRINGS WITH CENTRALIZER
Al-Mustansiriyah Journal of Science, 2020 In this paper we recall the definition of centralizer on inverse semiring. Also introduce the definition of Jordan ideal and Lie ideal. Some results of M.A.Joso Vukman on centralizers on semiprime rings are generalized here to inverse semirings.
Rawnaq Khaleel Ibraheem +1 more
doaj +1 more source
International Journal of Mathematics and Mathematical Sciences, 2000 For prime rings R, we characterize the set U∩CR([U,U]), where U is a right ideal of R; and we apply our result to obtain a commutativity-or-finiteness theorem. We include extensions to semiprime rings.
Howard E. Bell
doaj +1 more source
Rank of elements of general rings in connection with unit-regularity
, 2018 We define the rank of elements of general unital rings, discuss its properties and give several examples to support the definition. In semiprime rings we give a characterization of rank in terms of invertible elements.
Stopar, Nik
core +1 more source
Notes on Semiprime Ideals with Symmetric Bi-Derivation
AxiomsIn this paper, we prove many algebraic identities that include symmetric bi-derivation in rings which contain a semiprime ideal. We intend to generalize previous results obtained for semiprime rings with symmetric derivation using semiprime ideals in ...
Ali Yahya Hummdi +3 more
doaj +1 more source
On multiplicative centrally-extended maps on semi-prime rings
Journal of Taibah University for Science, 2022 In this paper, we show that for semi-prime rings of two-torsion free and 6-centrally torsion free, given a multiplicative centrally-extended derivation δ and a multiplicative centrally-extended epimorphism ϕ we can find a central ideal K and maps ...
M. S. Tammam EL-Sayiad, A. Ageeb
doaj +1 more source
A note on a pair of derivations of semiprime rings
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 +1 more source
On Skew Left n-Derivations with Lie Ideal Structure
مجلة بغداد للعلوم, 2019 In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and the commutativity of Lie ideal under certain conditions were proved.
Faraj et al.
doaj +1 more source
Prime Graphs of Polynomials and Power Series Over Noncommutative Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi +3 more
wiley +1 more source