Geodesic
The Fredholm Elements of a Ring
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 84-95

Voir la notice de l'article provenant de la source Cambridge University Press

In (1), Atkinson characterized the set of Fredholm operators on a Banach space X as those bounded operators invertible modulo the two-sided ideal of compact operators on X. It follows from this characterization that the Fredholm operators can also be described as those bounded operators which are invertible modulo the two-sided ideal of bounded operators on X which have finite-dimensional range. This ideal is the socle of the algebra of all bounded operators on X. Now, if A is any ring with no nilpotent left or right ideals, then the concept of socle makes sense (the socle of A in this case is the algebraic sum of the minimal left ideals of A, or 0 if A has no minimal left ideals). Also, in this case, the socle is a two-sided ideal of A. In this paper we study the elements in a ring A which are invertible modulo the socle. We call these elements the Fredholm elements of A. 
Barnes, Bruce Alan. The Fredholm Elements of a Ring. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 84-95. doi: 10.4153/CJM-1969-009-1
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