Prime Ring
Notes on Traces of a Symmetric Generalized (?, ?)-Biderivations and Commutativity in Prime Rings Auday Hekmat Mahmood
... Let R be a 2-torision free prime ring and U a nonzero ideal of R. Suppose G: R×R→R is a symmetric generalized Biderivation associated with a nonzero Biderivation D such that the Traces d and g of D and G ...
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On Ideals and Commutativity of Prime Rings with Generalized Derivations
... Theorem 3.1. Let R be a prime ring and I a nonzero left ideal of R. Suppose that R admits a generalized derivation F with associated derivation d of R such that d(Z(R)) 6= 0. Further, if R satisfies the ...
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Skew Commuting Derivations of Noncommutative Prime Rings
... a ring is commutative if and only if the only inner derivation on the ring is ...a ring with the set of matrices with entries in the ring (see, ...a ring is commutative, see ( ...
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Identities with derivations and automorphisms on semiprime rings
... The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ...
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On Commutativity of *-Prime Near-Rings with Derivations
... ∗-prime ring having nonzero ∗-ideal I then (i) If d is a nonzero derivation on R which commutes with ∗ and [x, R]Id(x) = {0} for all x ∈ I, then R is ...
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On (?,?)-Derivations and Commutativity of Prime and Semi prime ?-rings Afrah Mohammad Ibraheem
... called prime if aΓRΓb = 0 with a, b ∈R implies a = 0 or b = 0, and R is called semi prime if aΓRΓa = 0 with a ∈R implies a = ...semi-) prime Γ-ring is an extension for the notion of a ...
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Miguel Ferrero
... nil ring then R[x] is a Jacobson radical ...strongly prime (u-strongly prime, for short) radical. The u- strongly prime radical S(R) of a ring R is defined as the intersection of all ...
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Right orders in full linear rings
... with zero right singular ideal, but not an integral domain, if S contains uniform right ideals then S 1s a right quotient ring of any prime ring over which it 1s right... This result has[r] ...
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On Finite Rank Operators on Centrally Closed Semiprime Rings
... It is also well know that the extended centroid of a prime ring is a field, however, for a semiprime ring, we can only assert that said extended centroid is a von Neumann regular ring. This is ...
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Vol 5, No 3 (2014)
... artinian ring is commutative if it has commuting non-trivial ...a prime ring forces Ring to be commutative (Posner’s second ...a prime ring of characterstic different from two ...
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Product of derivations on C$^*$-algebras
... prime ring. He showed that if the product of two derivations on a prime ring, with characteristic not equal to 2, is a derivation then one of them must be equal to ...
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Vol 2, No 2 (2011)
... -prime ring with involution , U a non zero -Lie ideal and I a nonzero -ideal of ...-prime ring R admitting a generalized derivation F satisfying any of the following properties: ...
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The envelope of a subcategory in topology and group theory
... Reflective subcategories arise throughout mathematics, via several examples such as the free group, free ring, functors in algebra, various compactification functors in topology, and completion functors in ...
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Serial piecewise domains
... Noetherian ring is a piecewise domain if and only if it is right ...serial ring with right Noetherian diagonal is a piecewise domain if and only if it is ...
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A commutative Bezout \(PM^{\ast}\) domain is an elementary divisor ring
... Hermite ring is a Bezout ...Bezout ring are ...commutative ring R is an Hermite ring if and only if for all a, b ∈ R there exist a 1 , b 1 , d ∈ ...
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Right (θ,θ)-4-Derivations on Prime Near-Rings
... Suppose that N is a near –ring and is a mapping on N . This paper consists of two sections . In section one , we recall some basic definitions and other concepts , which will be used later in our paper , we ...
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On Semigroup Ideals and (Ɵ, Ɵ)-3-Derivations in Near-Rings
... Let N be a near –ring and is a mapping on N . This paper consists of two sections . In section one , we recall some basic definitions and other concepts , which be used in our paper , we explain these concepts by ...
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Non Noetherian unique factorisation rings
... W e will now prove another result which was only known in the Noetherian case, namely that if R is a Goldie U.F.D. then R is a maximal order. The proof is again based o n the proof of the Noetherian case (Theorem 2.10 ...
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Vol 4, No 2 (2013)
... 2-potent prime ideal in a Boolean like semi ring and establish various characterization of almost primary ideals in terms of 2-potent prime ideals, radical of an ...almost prime ideal of ...
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On Completely And Semi Completely Prime Ideal With Respect To An Element Of A Boolean 1, 2 Near-Ring
... near- ring and later 1930 Wieland has investigated it ...near ring can be found ...of prime ideals of a near-ring ...(semi) prime ideals of a near-ring ...semi prime ideal ...
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