One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summa...One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.展开更多
We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical space...We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.展开更多
文摘One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.
基金supported by University of Cyprus and New Function Spaces in Harmonic Analysis and Their Applications in Statistics(Individual Grant)。
文摘We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.
