Geodesic
On Very Large One Sided Ideals of a Ring
Canadian mathematical bulletin, Tome 9 (1966) no. 2, pp. 191-196

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

If R is a ring, a right (left) ideal of R is said to be large if it has non-zero intersection with each non-zero right (left) ideal of R [8]. If S is a set, let |S| be the cardinal number of S. We say a right (left) ideal I of a ring R is very large if |R/I| < < No. If a is an element of a ring R such that (a)r = {r ∊ R|ar = 0} is very large then we say a is very singular. The set of all very singular elements of a ring R is a two sided ideal of R. If R is a prime ring, then 0 is the only very singular element of R and a very large right (left) ideal of R is indeed large provided that R is not finite. 
Koh, Kwangil. On Very Large One Sided Ideals of a Ring. Canadian mathematical bulletin, Tome 9 (1966) no. 2, pp. 191-196. doi: 10.4153/CMB-1966-025-9
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