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On Functional Representations of a Ring without Nilpotent Elements

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh
Kwangil Koh*
Affiliation:
Tulane University, New Orleans, Louisiana; North Carolina State University, Raleigh, North Carolina
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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.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971, pp. 349 - 352
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Dauns, J. and Hofmann, K. H., Representation of rings by sections, Memoirs Amer. Math. Soc, 83, 1968.Google Scholar
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3. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966.Google Scholar
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5. Stewart, P. N., Semi-simple radical classes, Pacific J. Math. 32 (1970), 249-254.Google Scholar