Finite projectivity and contravariant finiteness

Authors:
K. Igusa, S. O. Smalø and G. Todorov

Journal:
Proc. Amer. Math. Soc. **109** (1990), 937-941

MSC:
Primary 16D90; Secondary 16E10, 18G20

DOI:
https://doi.org/10.1090/S0002-9939-1990-1027094-0

MathSciNet review:
1027094

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Abstract: Let be an artin algebra, let be the category of finitely generated , and let be the subcategory of consisting of the modules of projective dimension less than or equal to one. In this paper it is proved that if the projective dimension of the injective envelope of as a is less than or equal to one, then is contravariantly finite in . It also contains an example of finitistic projective dimension one where is not contravariantly finite in .

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1027094-0

Article copyright:
© Copyright 1990
American Mathematical Society