Stable tubes in extriangulated categories
Let be a semibrick in an extriangulated category. If is a -semibrick, then the Auslander-Reiten quiver of the filtration subcategory generated by is . If is a -cycle semibrick, then is .
Let be a semibrick in an extriangulated category. If is a -semibrick, then the Auslander-Reiten quiver of the filtration subcategory generated by is . If is a -cycle semibrick, then is .
In this note we show that for a -module, in particular, an almost -tilting module, over a ring with such that has finite flat dimension, the upper bound of the global dimension of can be estimated by the global dimension of and hence generalize the corresponding results in tilting theory and the ones in the theory of -modules. As an application, we show that for a finitely generated projective module over a VN regular ring , the global dimension of its endomorphism ring is not more...
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