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TRIVIAL MAXIMAL 1-ORTHOGONAL SUBCATEGORIES FOR AUSLANDER 1-GORENSTEIN ALGEBRAS

  • ZHAOYONG HUANG (a1) and XIAOJIN ZHANG (a2)
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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Copyright
COPYRIGHT: ©2013 Australian Mathematical Publishing Association Inc. 
Corresponding author
✉huangzy@nju.edu.cn
References
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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