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On the Dimension of Modules and Algebras, VI. Comparison of Global and Algebra Dimension

Published online by Cambridge University Press:  22 January 2016

Maurice Auslander
Maurice Auslander*
Affiliation:
University of Michigan
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Throughout this paper all rings are assumed to have unit elements. A ring Λ is said to be semi-primary if its Jacobson radical N is nilpotent and Г = Λ/N satisfies the minimum condition. The main objective of this paper is

THEOREM I. Let A be a semi-primary algebra over a field K. Let N be the radical of Λ and Г = Λ/N. If

Then

dim Λ = gl.dim Λ.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 11 , February 1957 , pp. 61 - 65
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Auslander, M., On the dimension of modules and algebras (III), global dimension, Nagoya Math. J., 9 (1955),67–77.CrossRefGoogle Scholar
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