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On a Class of Projective Modules Over Central Separable Algebras

Published online by Cambridge University Press:  20 November 2018

George Szeto
George Szeto*
Affiliation:
Bradley University, Peoria, Illinois
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In [5], DeMeyer extended one consequence of Wedderburn's theorem; that is, if R is a commutative ring with a finite number of maximal ideals (semi-local) and with no idempotents except 0 and 1 or if R is the ring of polynomials in one variable over a perfect field, then there is a unique (up to isomorphism) indecomposable finitely generated projective module over a central separable R-algebra A.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 415 - 417
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367-409.Google Scholar
2. Cartan, H. and Eilenberg, S., Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956.Google Scholar
3. Childs, L. N. and DeMeyer, F. R., On automorphisms of separable algebras, Pacific J. Math. 23 (1967), 25-34.Google Scholar
4. DeMeyer, F. R., On automorphisms of separable algebras II, Pacific J. Math. 32 (1970), 621-631.Google Scholar
5. DeMeyer, F. R., Projective modules over central separable algebras, Canad. J. Math. 21 (1969), 39-43.Google Scholar
6. Pierce, R. S., Modules over commutative regular rings, Mem. Amer. Math. Soc. No. 70, 1967.Google Scholar
7. Villamayor, O. and Zelinsky, D., Galois theory for rings with infinitely many idempotents, Nagoya Math. J. 35 (1969), 83-98.Google Scholar