Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a r...Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. （1988）.展开更多
Let R be a domain.In this paper,we show that if R is one dimensional,then R is a Noetherian Warfield domain if and only if every maximal ideal of R is 2-generated and for every maximal ideal M of R,M is divisorial in ...Let R be a domain.In this paper,we show that if R is one dimensional,then R is a Noetherian Warfield domain if and only if every maximal ideal of R is 2-generated and for every maximal ideal M of R,M is divisorial in the ring(M:M).We also prove that a Noetherian domain R is a Noetherian Warfield domain if and only if for every maximal ideal M of R,M^(2) can be generated by two elements.Finally,we give a sufficient condition under which all ideals of R are strongly Gorenstein projective.展开更多
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
文摘Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. （1988）.
基金This work was partially supported by the Department of Mathematics in Kyungpook National University and National Natural Science Foundation of China(Grant No.11671283)The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(2017R1C1B1008085),Korea.
文摘Let R be a domain.In this paper,we show that if R is one dimensional,then R is a Noetherian Warfield domain if and only if every maximal ideal of R is 2-generated and for every maximal ideal M of R,M is divisorial in the ring(M:M).We also prove that a Noetherian domain R is a Noetherian Warfield domain if and only if for every maximal ideal M of R,M^(2) can be generated by two elements.Finally,we give a sufficient condition under which all ideals of R are strongly Gorenstein projective.
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.
