Extremely noncommutative elements in rings

Howard E. Bell*, Abraham A. Klein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)19-24
Number of pages6
JournalMonatshefte fur Mathematik
Issue number1
StatePublished - Jan 2008


  • Centralizer
  • Extremely noncommutative element
  • Indecomposable ring
  • Peirce decomposition
  • Periodic ring
  • Potent element


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