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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1027094
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Abstract: Let $ \Lambda $ be an artin algebra, let $ \bmod \Lambda $ be the category of finitely generated $ \Lambda - {\text{modules}}$, and let $ p{d_1} \bmod \Lambda $ be the subcategory of $ \bmod \Lambda $ 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 $ \Lambda $ as a $ \Lambda - {\text{module}}$ is less than or equal to one, then $ p{d_1}\bmod \Lambda $ is contravariantly finite in $ \bmod \Lambda $. It also contains an example of finitistic projective dimension one where $ p{d_1}\bmod \Lambda $ is not contravariantly finite in $ \bmod \Lambda $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1027094-0
PII: S 0002-9939(1990)1027094-0
Article copyright: © Copyright 1990 American Mathematical Society