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On the Wedderburn Theorem

Published online by Cambridge University Press:  20 November 2018

George Szeto
George Szeto*
Affiliation:
Bradley University, Peoria, Illinois
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In [6], Pierce studied the modules over a commutative regular ring R by using the representation of R as the global sections of a sheaf which we call the Pierce sheaf. When the stalks of the Pierce sheaf are regular, Magid gave a Galois theory and some properties for a central separable R-algebra [4, (2.4), (2.5), (2.6) and (2.7)]. When the stalks of the Pierce sheaf are semi-local, DeMeyer presented a Galois theory for a central separable R-algebra [3, sections 2 and 3] and the author characterized the finitely generated and projective modules over a central separable R-algebra in terms of the R-modules in [7] and [8].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 525 - 530
Copyright
Copyright © Canadian Mathematical Society 1973

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. DeMeyer, F., Projective modules over central separable algebras, Can. J. Math. 21 (1969), 39–43.Google Scholar
3. DeMeyer, F., Automorphisms of separable algebras. II, Pacific J. Math. 32 (1970), 621–631.Google Scholar
4. Magid, A., Pierce's representation and separable algebras, Illinois J. Math. 15 (1971), 114–121.Google Scholar
5. Magid, A., Locally Galois algebras, Pacific J. Math. 33 (1970), 707–724.Google Scholar
6. Pierce, R., Modules over commutative regular rings, Mem. Amer. Math. Soc. 70 (1967).Google Scholar
7. Szeto, G., On a class of projective modules over central separable algebras, Can. Math. Bull. 14 (1971), 415–417.Google Scholar
8. Szeto, G., On a class of projective modules over central separable algebras. II, Can. Math. Bull. 15 (1972), 411–416.Google Scholar
9. Zelinsky, D. and Villamayor, O., Galois theory for rings with infinitely many idempotents, Nagoya Math. J. 35 (1969), 83–98.Google Scholar