Results 231 to 240 of about 22,083 (264)

Comparing Graded Versions of the Prime Radical

Canadian Mathematical Bulletin, 1991
AbstractLet G be a group with identity e, let λ be a normal supernilpotent radical in the category of associative rings and let λref be the reflected radical in the category of G-graded rings. Then for A a G-graded ring, λref(A) is the largest graded ideal of A whose intersection with Ae is λ (Ae). For λ = B, the prime radical, we compare Bref(A) to BG(
Beattie, M. A., Liu, S.-X., Stewart, P. N.   +2 more
openaire   +2 more sources

On orders with prime radical

Archiv der Mathematik, 1987
Two classical theorems for orders in semisimple \({\mathbb{Q}}\)-algebras are extended to the non-semisimple case: 1. the existence of maximal orders, and 2. the Jordan-Zassenhaus theorem. Ad 1: An order \(\Lambda\) in a \({\mathbb{Q}}\)-algebra A is said to be maximal if for any overorder \(\Gamma\) \(\supset \Lambda\) there exists an algebra ...
openaire   +2 more sources

Prime Radicals of Special Lie Superalgebras

Journal of Mathematical Sciences, 2005
It is well-known that an associative algebra graded by a finite group satisfies a polynomial identity if and only if its unitary component is a PI-algebra. It is proved that for a special Lie superalgebra \(L\) the superalgebra \(\text{ Ad}\, L\) is PI, i.e., \(L\) is a so-called generally special Lie superalgebra.
Balaba, I. N., Pikhtil'kov, S. A.
openaire   +2 more sources

Solvability by Real Radicals and Fermat Primes

Canadian Mathematical Bulletin, 2004
AbstractWe give a survey of old and new results concerning the expressibility of the real roots of a solvable polynomial over a real number field by real radicals. A characterization of Fermat primes is obtained in terms of solvability by real radicals for certain ploynomials.
openaire   +2 more sources

Topological prime radical of a group

Journal of Mathematical Sciences, 2007
A class \({\mathcal R}\) of groups is called radical if the following conditions are satisfied: 1) A homomorphic image of an \({\mathcal R}\)-group is an \({\mathcal R}\)-group. 2) Each group has an \({\mathcal R}\)-radical, i.e., a normal \({\mathcal R}\)-subgroup which contains all its other normal \({\mathcal R}\)-subgroups.
Bazigaran, B., Glavatskiĭ, S. T., Mikhalev, A. V.   +2 more
openaire   +2 more sources

On the Prime Radical of PI-Representable Groups

Mathematical Notes, 2002
The author calls a group \(G\) PI-representable if \(G\) is a subgroup of an associative \(F\)-algebra satisfying a polynomial identity, where \(F\) is a field. A normal subgroup \(P\) of \(G\) is called prime if whenever \(P\) contains the commutator \([A,B]\) of some normal subgroups \(A\) and \(B\), then \(P\) contains \(A\) or \(P\) contains \(B\).
openaire   +2 more sources

Prime radicals in sandwich near-rings

Acta Mathematica Hungarica, 2011
In some previous works [\textit{G. L. Booth} and \textit{P. R. Hall}, Beitr. Algebra Geom. 45, No. 1, 21-27 (2004; Zbl 1059.16037) and \textit{G. L. Booth}, ibid. 46, No. 1, 207-214 (2005; Zbl 1080.16045)] the author studied various kinds of primeness in near-rings and sandwich near-rings of continuous functions.
openaire   +1 more source

A topological prime quasi-radical

Journal of Mathematical Sciences, 2006
The authors define a topological prime quasi-radical \(\mu(R)\) of a topological ring \(R\) as the intersection of all closed prime ideals and present several examples showing that this concept is different from the topological Baer radical \(L(R)\) and from the set of all elements \(b\in R\) such that any \(m'\)-sequence which starts from \(b\) is ...
Bazigaran, B., Glavatsky, S. T., Mikhalev, A. V.   +2 more
openaire   +2 more sources

The Prime Radical of Alternative Rings and Loops

Journal of Mathematical Sciences, 2017
A characterization of the prime radical of loops as the set of strongly Engel elements is given. Connections between the prime radical of the loop of units of an alternative ring with unity and the prime radical of this ring are described.
openaire   +1 more source

ON RADICAL FIELD EXTENSIONS OF PRIME EXPONENT

Journal of Algebra and Its Applications, 2002
In this paper we investigate finite separable radical extensions K ⊆ L of prime exponent via the concept of G-Cogalois extension. As particular cases we retrieve some older results in I. Kaplansky [9] and A. Baker and H. M. Stark [7] concerning such radical extensions.
openaire   +1 more source