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- W4300859939 abstract "This article supplements recent work of the authors. (1) A criterion for failure of covariant finiteness of a full subcategory of $Lambdatext{-mod}$ is given, where $Lambda$ is a finite dimensional algebra. The criterion is applied to the category ${cal P}^{infty}(Lambdarm{-mod})$ of all finitely generated $Lambda$-modules of finite projective dimension, yielding a negative answer to the question whether ${cal P}^{infty}(Lambdarm{-mod})$ is always covariantly finite in $Lambdatext{-mod}$. Part (2) concerns contravariant finiteness of ${cal P}^{infty}(Lambdarm{-mod})$. An example is given where this condition fails, the failure being, however, curable via a sequence of one-point extensions. In particular, this example demonstrates that curing failure of contravariant finiteness of ${cal P}^{infty}(Lambdarm{-mod})$ usually involves a tradeoff with respect to other desirable qualities of the algebra." @default.
- W4300859939 created "2022-10-04" @default.
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- W4300859939 date "2014-07-08" @default.
- W4300859939 modified "2023-10-18" @default.
- W4300859939 title "Co- Versus Contravariant Finiteness of Categories of Representations" @default.
- W4300859939 doi "https://doi.org/10.48550/arxiv.1407.2300" @default.
- W4300859939 hasPublicationYear "2014" @default.
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