Remarks on Centers of Rings
| Autor: | Yang Lee, Tai Keun Kwak, Juan Huang, Hai-lan Jin, Zhelin Piao |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Reduced ring
Ring (mathematics) Algebra and Number Theory Mathematics::Commutative Algebra Computer Science::Information Retrieval Applied Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics A domain Triangular matrix Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 010103 numerical & computational mathematics Center (group theory) 01 natural sciences Combinatorics Full matrix Computer Science::General Literature 0101 mathematics Mathematics |
| Zdroj: | Algebra Colloquium. 28:1-12 |
| ISSN: | 0219-1733 1005-3867 |
| DOI: | 10.1142/s100538672100002x |
| Popis: | It is proved that for matrices [Formula: see text], [Formula: see text] in the [Formula: see text] by [Formula: see text] upper triangular matrix ring [Formula: see text] over a domain [Formula: see text], if [Formula: see text] is nonzero and central in [Formula: see text] then [Formula: see text]. The [Formula: see text] by [Formula: see text] full matrix rings over right Noetherian domains are also shown to have this property. In this article we treat a ring property that is a generalization of this result, and a ring with such a property is said to be weakly reversible-over-center. The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains. The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally. We also consider the connection between the property of being weakly reversible-over-center and the related ring properties. |
| Databáze: | OpenAIRE |
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