Annihilators of nilpotent elements

Abraham A. Klein

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-3

Abstract:

Let x be a nilpotent element of an infinite ring R (not necessarily with 1 ). We prove that A ( x ) —the two-sided annihilator of x —has a large intersection with any infinite ideal I of R in the sense that card ( A ( x ) ∩ I ) = card I . In particular, card A ( x ) = card R ; and this is applied to prove that if N is the set of nilpotent elements of R and R ≠ N , then card ( R \ N ) ≥ card N .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:151527

DOI: 10.1155/IJMMS.2005.3517

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