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A Note on Semihereditary Rings

Published online by Cambridge University Press:  20 November 2018

E. Enochs
E. Enochs*
Affiliation:
University of Kentucky, Lexington, Kentucky
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It's well known (see Endo [1]) that for a commutative ring A, if A is semihereditary then w.gl. dim. A ≤ 1. It seems worth recording the noncommutative version of this.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 439 - 440
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Endo, S., On semihereditary rings, J. Math. Soc. Japan 13 (1961), 109–119.Google Scholar
2. Maddox, B. H., Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155–158.Google Scholar
3. Cohn, P. M., On the free product of associative rings I, Math. Z. 71 (1959), 380–398.Google Scholar
4. Megibben, C., Absolutely pure modules, Proc. Amer. Math. Soc. 26 (1970), 561–566.Google Scholar
5. Lambek, J., A module is flat if and only if its character module is injective, Canad. Math. Bull. 7 (1964), 237–243.Google Scholar