Algebra
Generating regular elements
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 429-432.

Let R be a prime right Goldie ring. A useful fact is that, if a,bR are such that aR+bR contains a regular element, then there exists λR such that a+bλ is regular. We show that the analogous result holds for n1 pairs of elements: if R contains a field of cardinality at least n+1, and if ai,biR are such that aiR+biR contains a regular element for 1in, then there exists a single element λR such that ai+biλ is regular for each i.

Soit R un anneau de Goldie premier. Un résultat utile est que si a,bR sont tels que, aR+bR contienne un élément régulier, alors il existe λR tel que a+bλ est régulier. Nous montrons quʼun résultat analogue est vrai pour n1 paires de tels élément : si R contient un corps de cardinal >n et si les ai,biR sont tels que aiR+biR contienne un élément régulier, alors il existe λR tel que ai+biλ est régulier pour tout i.

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Published online:
DOI: 10.1016/j.crma.2013.06.001
Stafford, J.T. 1

1 School of Mathematics, Alan Turing Building, The University of Manchester, Oxford Road, Manchester M13 9PL, England, United Kingdom
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Stafford, J.T. Generating regular elements. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 429-432. doi : 10.1016/j.crma.2013.06.001. http://www.numdam.org/articles/10.1016/j.crma.2013.06.001/

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