Results 321 to 330 of about 44,957 (356)

*-PRIME GROUP RINGS

Journal of Algebra and Its Applications, 2009
In this paper we characterize *-prime group rings. We prove that the group ring RG of the group G over the ring R is *-prime if and only if R is *-prime and Λ+(G) = (1). In the process we obtain more examples of group rings which are *-prime but not strongly prime.
Joshi, Kanchan, Sharma, R. K., Srivastava, J. B.   +2 more
openaire   +1 more source

On the Multiplication Ring of a Prime Ring

Communications in Algebra, 2006
Given a positive integer n, we show there is a positive integer f(n) with the following property. Let R be a prime ring with extended centroid C, and let a 1,a 2,…,a n be C-independent elements of R. Then there is an element in the multiplication ring of R such that m ≤ f(n), p(a 1) = 0 and p(a 2),…,p(a n ) are C-independent. A similar approach is used
M Brešar
exaly   +2 more sources

A Class of Prime Rings

Canadian Mathematical Bulletin, 1966
If R is a ring and I is a right ideal of R then I is called faithful if R - I is a faithful right R-module, i.e. if { r ∊ R: Rr⊆ I} = (0). I is called irreducible [ 1 ] provided that if J1 and J2 are right ideals such that J1 ∩ J2 = I, then J1 or J2 = I. Let N(I){ r ∊ R: rI⊆ I} and [ I: a ] = { r ∊ R: ar⊆ I} for a ∊ R. We write (a)r for [(0): a ].
Koh, K., Mewborn, A. C.
openaire   +1 more source

Derivations in Prime Rings

Canadian Mathematical Bulletin, 1983
AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
openaire   +2 more sources

Prime Ideals in Near-Rings

Results in Mathematics, 1993
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Birkenmeier, Gary, Heatherly, Henry, Lee, Enoch   +2 more
openaire   +1 more source

On Compact Prime Rings and their Rings of Quotients

Canadian Mathematical Bulletin, 1968
In [10], it is defined that a right (or left) ideal I of a ring R is very large if the cardinality of R/I is finite. It is also proven in [10, Theorem 3.4] that if R is a prime ring with 1 such that its characteristic is zero, then R is a right order in a simple ring with the minimum condition on one sided ideals if every large right ideal of R is very
openaire   +1 more source

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

Skew Derivations of Prime Rings

Siberian Mathematical Journal, 2006
Summary: Given a prime ring \(R\), a skew \(g\)-derivation for \(g\colon R\to R\) is an additive map \(f\colon R\to R\) such that \(f(xy)=f(x)g(y)+xf(y)=f(x)y+g(x)f(y)\) and \(f(g(x))=g(f(x))\) for all \(x,y\in R\). We generalize some properties of prime rings with derivations to the class of prime rings with skew derivations.
openaire   +2 more sources

Prime and homogeneous rings and algebras

Algebra i logika, 2019
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openaire   +1 more source