no. 11-12
Algebra
Generating regular elements
[Engendrer des éléments réguliers]

Présenté par : Michèle Vergne

Stafford, J.T.1
1 School of Mathematics, Alan Turing Building, The University of Manchester, Oxford Road, Manchester M13 9PL, England, United Kingdom
Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 429-432.

Soit R un anneau de Goldie premier. Un résultat utile est que si a,b∈R sont tels que, aR+bR contienne un élément régulier, alors il existe λ∈R tel que a+bλ est régulier. Nous montrons quʼun résultat analogue est vrai pour n⩾1 paires de tels élément : si R contient un corps de cardinal >n et si les ai,bi∈R sont tels que aiR+biR contienne un élément régulier, alors il existe λ∈R tel que ai+biλ est régulier pour tout i.

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

Reçu le :
Accepté le :
Publié le :
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, Tome 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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