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Estimates of global dimension

Wei Jiaqun — 2006

Czechoslovak Mathematical Journal

In this note we show that for a * n -module, in particular, an almost n -tilting module, P over a ring R with A = E n d R P such that P A has finite flat dimension, the upper bound of the global dimension of A can be estimated by the global dimension of R 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 R , the global dimension of its endomorphism ring is not more...

Recollements induced by good (co)silting dg-modules

Rongmin ZhuJiaqun Wei — 2023

Czechoslovak Mathematical Journal

Let U be a dg- A -module, B the endomorphism dg-algebra of U . We know that if U is a good silting object, then there exist a dg-algebra C and a recollement among the derived categories 𝐃 ( C , d ) of C , 𝐃 ( B , d ) of B and 𝐃 ( A , d ) of A . We investigate the condition under which the induced dg-algebra C is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained. Finally, some...

Stable tubes in extriangulated categories

Li WangJiaqun WeiHaicheng Zhang — 2022

Czechoslovak Mathematical Journal

Let 𝒳 be a semibrick in an extriangulated category. If 𝒳 is a τ -semibrick, then the Auslander-Reiten quiver Γ ( ( 𝒳 ) ) of the filtration subcategory ( 𝒳 ) generated by 𝒳 is 𝔸 . If 𝒳 = { X i } i = 1 t is a τ -cycle semibrick, then Γ ( ( 𝒳 ) ) is 𝔸 / τ 𝔸 t .

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