For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and duali...For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.展开更多
Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω（...Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω（S）, where Ω（S）is the Loop category of（S）,and the structure of K<sub>1</sub>S is given.展开更多
In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of fi...In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of finitely generated nilpotent groups with central associated subgroups are weakly potent.展开更多
In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to character...In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.展开更多
In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated...In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.展开更多
文摘For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.
文摘Let S be a semigroup with identity and zero,（S）the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω（S）, where Ω（S）is the Loop category of（S）,and the structure of K<sub>1</sub>S is given.
文摘In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of finitely generated nilpotent groups with central associated subgroups are weakly potent.
文摘In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.
文摘In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
