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Semiprime Torsion Free Rings

Semiprime Torsion Free Rings
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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
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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
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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
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The structure of S-semiprime ideals and submodules in noncommutative rings

Communications in Algebra
This paper introduces the concept of right S-semiprime ideals and right S-semiprime submodules in the context of noncommutative rings. We investigate the properties of right S-semiprime ideals (submodules), providing multiple equivalent definitions and ...
Alaa Abouhalaka, Nico Groenewald
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On Derivations in Semiprime Rings

Algebras and Representation Theory, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali, Shakir, Huang, Shuliang
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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
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Distributive semiprime rings

Mathematical Notes, 1995
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Certain basic functional identities of semiprime rings

Communications in Algebra, 2019
The goal of the article is to discuss certain basic functional identities of semiprime rings. Specifically, the following result is proved: Let R be a semiprime ring with extended centroid C and let be additive maps, where denotes the maximal left ring ...
Tsiu-Kwen Lee
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SEMIPRIME LEFT QUASI-MORPHIC RINGS

Journal of Algebra and Its Applications, 2013
A ring R is called left quasi-morphic if {Ra ∣ a ∈ R} = {l(b)∣ b ∈ R} where l(b) denotes the left annihilator of b. In 2007 Camillo and Nicholson showed that if R is quasi-morphic (left and right) and satisfies the ACC on {Ra ∣ a ∈ R}, then R is an artinian principal ideal ring. This is a new characterization of these rings.
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