TRIVIAL MAXIMAL 1-ORTHOGONAL SUBCATEGORIES FOR AUSLANDER 1-GORENSTEIN ALGEBRAS
2013 ◽
Vol 94
(1)
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pp. 133-144
Keyword(s):
AbstractLet $\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.
2019 ◽
Vol 18
(06)
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pp. 1950112
2016 ◽
Vol 26
(08)
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pp. 1597-1615
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1995 ◽
Vol 37
(2)
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pp. 191-204
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Keyword(s):
1994 ◽
Vol 36
(3)
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pp. 347-354
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2014 ◽
Vol 56
(3)
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pp. 551-568
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Keyword(s):
2017 ◽
Vol 10
(03)
◽
pp. 1750048
1992 ◽
Vol 34
(3)
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pp. 277-300
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2019 ◽
Vol 19
(09)
◽
pp. 2050174