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Absolute Purity

Published online by Cambridge University Press:  20 November 2018

David J. Fieldhouse
David J. Fieldhouse*
Affiliation:
University of Guelph, Guelph, Ontario
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Throughout this paper we use the Bourbaki [1] conventions for rings and modules: all rings are associative but not necessarily commutative and have a 1; all modules are unital.

Our purpose is to extend and simplify some recent results of Maddox [7], Megibben [8], Enochs [3], and the author [5] on absolutely pure modules by introducing several new dimensions, and using the absolutely pure dimension introduced by the author in [6], This completes some work on character modules and dimension in [5] and [6].

An A -module will be called an FFR-module if and only if it has a resolution by finitely generated free A -modules.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 6 - 10
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bourbaki, N., Algèbre commutative, Chapter 1 (Hermann, Paris, 1961).Google Scholar
2. Cartan-Eilenberg, , Homological algebra (Princeton Univ. Press, Princeton, 1956).Google Scholar
3. Enochs, E., On absolutely pure modules (to appear).Google Scholar
4. Fieldhouse, D., Pure theories, Math. Ann. 189 (1969), 1–18.Google Scholar
5. Fieldhouse, D., Character modules, Comment. Math. Helv. 46 (1971), 274–276.Google Scholar
6. Fieldhouse, D., Character modules, dimension, and purity (to appear).Google Scholar
7. Maddox, B., Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155–158.Google Scholar
8. Megibben, C., Absolutely pure modules, Proc. Amer. Math. Soc. 26 (1970), 561–566.Google Scholar