An extension of the Jacobson radical

Brown, Bailey

doi:10.1090/s0002-9939-1951-0040286-8

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The Graded Brown-mccoy Radical1

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1953

2016

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Cited by 10 publications

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“…It suffices now to prove that Ǐ is a modular ideal of A. Since I is a modular right ideal of A, we have that Ǐ = {a ∈ A | Aa ⊆ I}, by analogy with classical rings (see, for instance, [5]). We already know that there exists a ′ ∈ A such that ma ′ = m for every m ∈ M, and particularly, xa ′ = x.…”

Section: The Graded Brown-mccoy Radicalmentioning

confidence: 99%

On graded Brown–McCoy radicals of graded rings

Ilić-Georgijević

2016

J. Algebra Appl.

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We investigate the graded Brown-McCoy and the classical Brown-McCoy radical of a graded ring, which is the direct sum of a family of its additive subgroups indexed by a nonempty set, under the assumption that the product of homogeneous elements is again homogeneous. There are two kinds of the graded Brown-McCoy radical, the graded Brown-McCoy and the large graded Brown-McCoy radical of a graded ring. Several characterizations of the graded Brown-McCoy radical are given, and it is proved that the large graded Brown-McCoy radical of a graded ring is the largest homogeneous ideal contained in the classical Brown-McCoy radical of that ring.

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Section: The Graded Brown-mccoy Radicalmentioning

confidence: 99%