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TRIVIAL MAXIMAL 1-ORTHOGONAL SUBCATEGORIES FOR AUSLANDER 1-GORENSTEIN ALGEBRAS
Published online by Cambridge University Press: 28 February 2013
Abstract
Let $\Lambda $ be an Auslander 1-Gorenstein Artinian algebra with global dimension two. If $\Lambda $ admits a trivial maximal 1-orthogonal subcategory of $\text{mod } \Lambda $, then, for any indecomposable module $M\in \text{mod } \Lambda $, the projective dimension of $M$ is equal to one if and only if its injective dimension is also equal to one, and $M$ is injective if the projective dimension of $M$ is equal to two. In this case, we further get that $\Lambda $ is a tilted algebra.
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- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 94 , Issue 1 , February 2013 , pp. 133 - 144
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.