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K0 D’Un Anneau Dont Les Localises Centraux Sont Simples Artiniens

Published online by Cambridge University Press:  20 November 2018

W. D. Burgess
Affiliation:
Université d'Ottawa, Ottawa, Canada
J.-M. Goursaud
Affiliation:
Université de Poitiers, Poitiers, France
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Abstract

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The purpose of the note is to calculate the group K0(A) where A is a ring all of whose Pierce stalks are simple artinian. This generalizes known results for A self injective of type In. For A regular, with injective hull, Â, of type In, a characterization is given for when AÂ it induces an isomorphism K0(A) → K0(Â).

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Burgess, W. D. et Stephenson, W., Pierce sheaves of non-commutative rings. Comm. Algebra, 4 (1976), 51-75.Google Scholar
2. Goodearl, K. R., Von Neumann Regular Rings. Pitman, Londres, 1979.Google Scholar
3. Goodearl, K. R., Handelman, D. et Lawrence, J., Affine representations of Grothendieck groups and applications to Rickart C*-algebras and ℵ0-continuous regular rings, Memoirs Amer. Math. Soc. 234 (1980).Google Scholar
4. Goursaud, J.-M. et Jérémy, L., Sur l'enveloppe injective des anneaux réguliers, Comm. Algebra, 3 (1975), 763-779.Google Scholar
5. Handelman, D., K0 of von Neumann and AFC* algebras, Quart. J. Math. Oxford, 29 (1978), 427-441.Google Scholar
6. Lambek, J., Lectures on Rings and Modules. Blaisdell, Waltham, Mass., Toronto, Londres, 1966.Google Scholar
7. Pierce, R. S., Modules over commutative regular rings, Mémoires Amer. Math. Soc, 70 (1967).Google Scholar