A Property Satisfying Reducedness over Centers
| Autor: | Hai-lan Jin, Yang Lee, Tai Keun Kwak, Zhelin Piao |
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| Rok vydání: | 2021 |
| Předmět: |
Ring (mathematics)
Pure mathematics Algebra and Number Theory Property (philosophy) Mathematics::Commutative Algebra Applied Mathematics Polynomial ring Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Commutative ring Computer Science::General Literature Center (algebra and category theory) Commutative property Mathematics |
| Zdroj: | Algebra Colloquium. 28:453-468 |
| ISSN: | 0219-1733 1005-3867 |
| DOI: | 10.1142/s1005386721000353 |
| Popis: | This article concerns a ring property called pseudo-reduced-over-center that is satisfied by free algebras over commutative reduced rings. The properties of radicals of pseudo-reduced-over-center rings are investigated, especially related to polynomial rings. It is proved that for pseudo-reduced-over-center rings of nonzero characteristic, the centers and the pseudo-reduced-over-center property are preserved through factor rings modulo nil ideals. For a locally finite ring [Formula: see text], it is proved that if [Formula: see text] is pseudo-reduced-over-center, then [Formula: see text] is commutative and [Formula: see text] is a commutative regular ring with [Formula: see text] nil, where [Formula: see text] is the Jacobson radical of [Formula: see text]. |
| Databáze: | OpenAIRE |
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