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 denotes the class of all Warfield cotorsion R-mod...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 denotes the class of all Warfield cotorsion R-modules and P_(w_(∞))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.展开更多
基金This work was partially supported by the Sichuan Science and Technology Program(2023NSFSC0074)the National Natural Science Foundation of China(11961050,12061001)Aba Teachers University(ASS20230106,20210403005,20220301016).
文摘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 denotes the class of all Warfield cotorsion R-modules and P_(w_(∞))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.
