查看更多>>摘要：Let R be a commutative domain with 1 and Q(≠R)its field of quotients.In this note an R-module M is called w∞-Warfield cotorsion if M ∈ WC ∩P⊥w∞,where WC de-notes the class of all Warfield cotorsion R-modules and Pw∞ the class of all w∞-projective R-modules.It is shown that R is a PVMD if and only if all w-cotorsion R-modules are w∞-Warfield cotorsion,and that R is a Krull domain if and only if every w-Matlis cotorsion strong w-module over R is a w∞-Warfield cotorsion w-module.
查看更多>>摘要：In this paper,we prove a reduction result on wide subcategories of abelian categories which is similar to the Calabi-Yau reduction,silting reduction and τ-tilting re-duction.More precisely,if an abelian category A admits a recollement relative to abelian categories A'and A",which is denoted by(A',A,A",i*,i*,i!,j!,j*,j*),then the assign-ment C → j*(C)defines a bijection between wide subcategories in A containing i*(A')and wide subcategories in A".Moreover,a wide subcategory C of A containing i*(A')admits a new recollement relative to A'andj*(C)which is induced from the original recollement.
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