[PDF][PDF] Rings in which nilpotents belong to Jacobson radical
H Chen, O Gurgun, S Halicioglu… - … Univ. Al. I. Cuza Iasi. Mat …, 2016 - researchgate.net
H Chen, O Gurgun, S Halicioglu, A Harmanci
An. Stiint. Univ. Al. I. Cuza Iasi. Mat.(NS), 2016•researchgate.netLet R be a ring with identity and J (R) denote the Jacobson radical of R. A ring R is called J-
reduced if an= 0 (n∈ N) implies a∈ J (R) for any a∈ R. We give, in this article, many
characterizations of such rings. We construct some families of J-reduced rings. Furthermore,
the transposes of invertible matrices over such rings are studied.
reduced if an= 0 (n∈ N) implies a∈ J (R) for any a∈ R. We give, in this article, many
characterizations of such rings. We construct some families of J-reduced rings. Furthermore,
the transposes of invertible matrices over such rings are studied.
Abstract
Let R be a ring with identity and J (R) denote the Jacobson radical of R. A ring R is called J-reduced if an= 0 (n∈ N) implies a∈ J (R) for any a∈ R. We give, in this article, many characterizations of such rings. We construct some families of J-reduced rings. Furthermore, the transposes of invertible matrices over such rings are studied.
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