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- Title
On the condition that powers preserve noncentralness.
- Authors
Chen, Hongying; Huang, Juan; Kwak, Tai Keun; Lee, Yang
- Abstract
Jacobson investigated the structure of rings with the property that some power of each element is central, in the procedure of the study of commutativity. In this paper, we consider a class of rings in which this property occurs only for central elements, and such rings are called ppnc. We first prove that a noncommutative ppnc ring is infinite, and that a ppnc ring is commutative when it is a K-ring or a locally finite ring. We next study the structure of ppnc rings, and the relation between ppnc rings and related concepts (for example, K-rings, commutative rings and NI rings), through matrix rings, polynomial rings, right quotient rings and direct products.
- Subjects
QUOTIENT rings; NONCOMMUTATIVE rings; FINITE rings; COMMUTATIVE rings; MATRIX rings
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 11, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823502419