One-sided duo property on nilpotents
| Autor: | Hong Kee Kim, Tai Keun Kwak, Chan Yong Hong, Nam Kyun Kim, Yang Lee |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
right (left) nilpotent-duo ring nilpotent right (left) duo ring radical NI ring matrix ring ascending chain condition on left (right) annihilators Matematik Ring theory Ring (mathematics) Algebra and Number Theory Conjecture Mathematics::Commutative Algebra Polynomial ring Mathematics::Rings and Algebras Commutative ring Subring Matrix ring Combinatorics Mathematics::Group Theory Nilpotent Geometry and Topology Mathematics::Representation Theory Mathematics Analysis Computer Science::Cryptography and Security |
| Zdroj: | Volume: 49, Issue: 6 1974-1987 Hacettepe Journal of Mathematics and Statistics |
| ISSN: | 2651-477X |
| DOI: | 10.15672/hujms.571016 |
| Popis: | We study the structure of nilpotents in relation with a ring property that is near to one-sided duo rings. Such a property is said to be one-sided nilpotent-duo. We prove the following for a one-sided nilpotent-duo ring $R$: (i) The set of nilpotents in $R$ forms a subring; (ii) Köthe's conjecture holds for $R$; (iii) the subring generated by the identity and the set of nilpotents in $R$ is a one-sided duo ring; (iv) if the polynomial ring $R[x]$ over $R$ is one-sided nilpotent-duo then the set of nilpotents in $R$ forms a commutative ring, and $R[x]$ is an NI ring. Several connections between one-sided nilpotent-duo and one-sided duo are given. The structure of one-sided nilpotent-duo rings is also studied in various situations in ring theory. Especially we investigate several kinds of conditions under which one-sided nilpotent-duo rings are NI. |
| Databáze: | OpenAIRE |
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