Abstract
We study rings and K-algebras in which all elements or all noncentral elements have smallest possible centralizer. Our principal result asserts that a ring R must be either finite or commutative if each noncentral element a has centralizer equal to the subring generated by a.
Original language | English |
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Pages (from-to) | 19-24 |
Number of pages | 6 |
Journal | Monatshefte fur Mathematik |
Volume | 153 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2008 |
Keywords
- Centralizer
- Extremely noncommutative element
- Indecomposable ring
- Peirce decomposition
- Periodic ring
- Potent element