Results 271 to 280 of about 89,695 (313)

A Note on Radical Extensions of Rings

Canadian Mathematical Bulletin, 1975
All rings are associative. A ring T is said to be radical over a subring R if for every t ∈ T, there exists a natural number n(t) such that tn(t) ∈ R.In [1] Faith showed that if T is radical over R and T is primitive, then R is primitive. We might then ask if the same is true if prime is substituted for primitive.
Chacron, M., Lawrence, J., Madison, D.
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On the Adjoint Group of a Radical Ring

Canadian Mathematical Bulletin, 1995
AbstractThe relations between the adjoint group and the additive group of a radical ring and its nilpotency are investigated. It is shown that certain finiteness conditions carry over from the adjoint group to the additive group and that the converse holds for the class of minimax groups.
Amberg, Bernhard, Dickenschied, Oliver
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Radicals of a ring

Communications in Algebra, 1994
The paper concerns a description of ideals of a ring R which are radicals of R, i.e., they are of the form S(R), where S is a radical property of rings. This problem was already studied in a number of papers. For instance, in [4, 5] all radicals of Dedekind domains were described whereas in [3] some global properties of the set of hereditary radicals ...
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The Centers of a Radical Ring

Canadian Mathematical Bulletin, 1992
AbstractIt is shown that the nth center of a radical ring coincides with that of its adjoint group, from which a result of Jennings is sharpened and a conjecture of his is confirmed.
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Subgroups of the Adjoint Group of a Radical Ring

Canadian Journal of Mathematics, 1998
AbstractIt is shown that the adjoint group R° of an arbitrary radical ring R has a series with abelian factors and that its finite subgroups are nilpotent. Moreover, some criteria for subgroups of R° to be locally nilpotent are given.
Amberg, B., Dickenschied, O., Sysak, Ya. P.   +2 more
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The Artin radical of a Noetherian ring

Journal of the Australian Mathematical Society, 1977
AbstractIn this note we define the Artin radical of a Noetherian ring and describe some of its applications.
Chatters, A. W., Hajarnavis, C. R., Norton, N. C.   +2 more
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On the Periodic Radical of a Ring

Canadian Mathematical Bulletin, 1995
AbstractLet R be a ring and P(R) the sum of all periodic ideals of R. We prove that P(R) is the intersection of all prime ideals Pα such that contains no nontrivial periodic ideals. We also prove that P(R) = 0 if and only if Rs is a subdirect product of prime rings Rα with P(Rα) = 0.
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THE FACTOR RING OF A QUASI-BAER RING BY ITS PRIME RADICAL

Journal of Algebra and Its Applications, 2011
The quasi-Baer condition of R/P(R) is investigated when R is a quasi-Baer ring, where P(R) is the prime radical of R. We provide an example of quasi-Baer ring R such that R/P(R) is not quasi-Baer. However, when P(R) is nilpotent, we prove that if R is a quasi-Baer (resp., Baer) ring, then R/P(R) is quasi-Baer (resp., Baer).
Birkenmeier, Gary F., Kim, Jin Yong, Park, Jae Keol   +2 more
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The Jacobson radical of a band ring

Mathematical Proceedings of the Cambridge Philosophical Society, 1989
A band is a semigroup in which every element is idempotent. In this note we give an explicit description of the Jacobson radical of the semigroup ring of a band over a ring with unity. It is shown, further, that this radical is nil if and only if the Jacobson radical of the coefficient ring is nil.
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On the centers of a radical ring

Archiv der Mathematik, 1993
Let \((R,+,\circ)\) be the associated Lie ring and \((R,*)\) the adjoint group of a radical ring \(R\). It is shown that the upper central chain of the Lie ring \((R,+,\circ)\) and the upper \((R,*)\)-stable chain of the module \((R,+)\) are equal at each step.
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