Abstract
Let J(R) denotes the Jacobson radical of a ring R. We call a ring R a J-domain if the product of any two elements of \(R\setminus J(R)\) is non-zero. For a positive integer n, we prove that \(\mathbb {Z}_{n}\) is a J-domain if and only if n is a power of a prime number. Some extensions of J-domains such as polynomial rings, Nagata extension, subrings of matrix rings are investigated. This paper provides some conditions for a J-domain to be a reduced ring and a division ring. Furthermore, it is proved that the polynomial ring over a J-domain need not be J-domain.
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Roy, D., Subba, S. & Subedi, T. Domain property of rings relative to the Jacobson radical. Ann Univ Ferrara 69, 195–202 (2023). https://doi.org/10.1007/s11565-022-00411-y
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DOI: https://doi.org/10.1007/s11565-022-00411-y