A note on essential Ikeda-Nakayama rings (Q2120252)
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scientific article
| Language | Label | Description | Also known as |
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| English | A note on essential Ikeda-Nakayama rings |
scientific article |
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A note on essential Ikeda-Nakayama rings (English)
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31 March 2022
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This paper is a contribution to the ideal theory of non-commutative rings. A ring \(R\) is called Essential Ikeda-Nakayama (EIN) if for any two ideals \(I\) and \(J\), the sum of the left annihilators \(\ell(I)+\ell(J)\) is essential in \(\ell(I\cup J)\). The authors study the closure of EIN rings under direct products, polynomial rings, left triangular matrices and adjunction of identity, and the properties of non-singular EIN rings. They show that every semiprime ring is EIN.
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(IN)-ring
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right annihilator
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closed ideal
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EIN-ring
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