Geodesic
On Functional Representations of a Ring without Nilpotent Elements
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 349-352

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

In [3, p. 149], J. Lambek gives a proof of a theorem, essentially due to Grothendieck and Dieudonne, that if R is a commutative ring with 1 then R is isomorphic to the ring of global sections of a sheaf over the prime ideal space of R where a stalk of the sheaf is of the form R/0P , for each prime ideal P, and . In this note we will show, this type of representation of a noncommutative ring is possible if the ring contains no nonzero nilpotent elements. 
Koh, Kwangil. On Functional Representations of a Ring without Nilpotent Elements. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 349-352. doi: 10.4153/CMB-1971-063-7
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[1] 1. Dauns, J. and Hofmann, K. H., Representation of rings by sections, Memoirs Amer. Math. Soc, 83, 1968. Google Scholar

[2] 2. Koh, K., A note on a certain class of prime rings, Amer. Math. Monthly, 72, 1965. Google Scholar

[3] 3. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. Google Scholar

[4] 4. Pierce, R. S., Modules over commutative regular rings, Memoirs Amer. Math. Soc, 70. 1967. Google Scholar

[5] 5. Stewart, P. N., Semi-simple radical classes, Pacific J. Math. 32 (1970), 249-254. Google Scholar

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