On the closedness of taking injective hulls of several Serre subcategories

Belshoff and Xu showed that every Matlis reflexive module has a Matlis reflexive injective hull if and only if R is complete and has dimension less than or equal to 1. In this paper, we give a characterization of the closedness of taking injective hulls for a Serre subcategory consisting of Minimax modules. In addition, the closedness of taking injective hulls for a Serre subcategory consisting of extension modules of finitely generated modules by modules with finite support is characterized by the number of prime ideals. Our results provide a negative answer to Aghapournahr and Melkersson’s question concerning Melkersson subcategories.     

Strongly FP-injective modules

A module M is called strongly FP-injective if Extⁱ(P,M) = 0 for any finitely presented module P and all i≥1. (Pre)envelopes and (pre)covers by strongly FP-injective modules are studied. We also use these modules to characterize coherent rings. An example is given to show that (strongly) FP-injective (pre)covers may fail to be exist in general. We also give an example of a module that is FP-injective but not strongly FP-injective.     

The diagram for endomorphism algebras of two-term tilting complexes over self-injective algebras

We construct a diagram between the endomorphism algebra of a two-term projective module complex over a self-injective algebra and the endomorphism algebras of its homology groups and apply the diagram to the tilting theory of self-injective algebras. We give an example of recovering the endomorphism algebra of a two-term tilting complex over a self-injective algebra from the endomorphism algebras of its homology groups with some additional structures which appear in the diagram.     

Artinianess of graded local cohomology modules

Let be a Noetherian homogeneous ring with local base ring and let be a finitely generated graded -module. Let be the largest integer such that is not Artinian. We will prove that are Artinian for all and there exists a polynomial of degree less than such that for all . Let be the first integer such that the local cohomology module is not cofinite. We will show that for all the graded module is Artinian.

     

Projective Resolutions and Yoneda Algebras for Algebras of Dihedral Type

This paper provides a method for the computation of Yoneda algebras for algebras of dihedral type. The Yoneda algebras for one infinite family of algebras of dihedral type (the family in K. Erdmann’s notation) are computed. The minimal projective resolutions of simple modules were calculated by an original computer program implemented by one of the authors in C++ language. The algorithm of the program is based on a diagrammatic method presented in this paper and inspired by that of D. Benson and J. Carlson. This work was partially supported by the grant 06-01-00200 of the Russian Foundation for Basic Research.     

Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrices

Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d（y） and weak A-forms of wUq^d（y）.     

Highly flexible and excellent performance continuous carbon nanotube fibrous thermoelectric modules for diversified applications

A highly flexible and continuous fibrous thermoelectric (TE) module with high-performance has been fabricated based on an ultra-long single-walled carbon nanotube fiber, which effectively avoids the drawbacks of traditional inorganic TE based modules. The maximum output power density of a 1-cm long fibrous TE module with 8 p-n pairs can reach to 3436 μW·cm^-2, the power per unit weight to 2034 μW·g^-1, at a steady-state temperature difference of 50 K. The continuous fibrous TE module is used to detect temperature change of a single point, which exhibits a good responsiveness and excellent stability. Because of its adjustability in length, the flexible fibrous TE module can satisfy the transformation of the temperature difference between two distant heat sources into electrical energy. Based on the signal of the as-fabricated TE module, a multi-region recognizer has been designed and demonstrated. The highly flexible and continuous fibrous TE module with excellent performance shows a great potential in diversified applications of TE generation, temperature detection, and position identification.     

EXTENSlONS OF HARDY MODULES OVER THE POLYDISK ALGEBRA

1.IntroductionAHilbertmoduleisaHilbertspaceHwhichisalsoamoduleoverafunctionalgebraA,i.e.,thereisanassociativebilinearmultiplicationAxHHwhichiscontinuousinbothvariables.ThefirstsystematicstudyofHilbertmodulesappearedinthemonographofDouglasandPoulsen[...     

EXTENSIONS OF HARDY MODULES OVER THE POLYDISK ALGEBRA

In this paper, the Ext groups of Hardy modules over the polydisk algebra A(D^n) are calculated, Of particular importance is that the calculating of Ext-groups is closely related to harmonic analysis of polydisks. Finally, the authors point out that Ext-groups reveal rigidity of Hardy submodules over A(D^n) for n > 1.     

在无单位元下体现零模

本文用Horn函子刻划阿丁环．