On Gorenstein Projective Dimensions of Unbounded Complexes

Let R → S be a ring homomorphism and X be a complex of R-modules. Then the complex of S-modules S?_R~L X in the derived category D(S) is constructed in the natural way. This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X(possibly unbounded) with those of the S-complex S?_R~L X.It is shown that if R is a Noetherian ring of finite Krull dimension and φ : R → S is a faithfully flat ring homomorphism, then for any homologically degree-wise finite complex X, there is an equality Gpd_RX = GpdS(S?_R~L X). Similar result is obtained for Ding projective dimension of the S-complex S?_R~L X.     

Injective and automorphism-invariant non-singular modules

Every automorphism-invariant non-singular right A-module is injective if and only if the factor ring of the ring A with respect to its right Goldie radical is a right strongly semiprime ring.     

Change of grading,injective dimension and dualizing complexes

Let G,H be groups, φ:G→H a group morphism, and A a G-graded algebra. The morphism φ induces an H-grading on A, and on any G-graded A-module, which thus becomes an H-graded A-module. Given an injective G-graded A-module, we give bounds for its injective dimension when seen as H-graded A-module. Following ideas by Van den Bergh, we give an application of our results to the stability of dualizing complexes through change of grading.     

Amenable representations and finite injective von Neumann algebras

Let be the unitary group of a finite, injective von Neumann algebra . We observe that any subrepresentation of a group representation into is amenable in the sense of Bekka; this yields short proofs of two known results-one by Robertson, one by Haagerup-concerning group representations into .

     

Covers of algebraic varieties III. The discriminant of a cover of degree 4 and the trigonal construction

For each Gorenstein cover of degree we define a scheme and a generically finite map of degree called the discriminant of . Using this construction we deal with smooth degree covers with . Moreover we also generalize the trigonal construction of S. Recillas.

     

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??In this paper, we prove the existence and uniqueness of solutions for reflected backward stochastic differential equations driven by a Levy process, in which the reflecting barriers are just right continuous with left limits whose jumps are arbitrary. To derive the above results, the monotonic limit theorem of Backward SDE associated with Levy process is established.     

Ideals defining Gorenstein rings are (almost) never products

This note proves that if is an unramified regular local ring and proper ideals of height at least two, then is never Gorenstein.

     

由几何反演导出的分形几何

本文介绍了由几何反演而导出的自反分形概念.构造了一个对称的,分叉自反分形曲线和一个自反分形尘集.推广了分形密切的概念而且提出了一个新的概念——分形包络.最后给出了“肥皂”和“鸡蛋”的两个自反分形的实例.     

长度有限的模的对偶

本文推广了局部对偶理论并讨论了长度为有限的模的同调维数．     

Upper and Lower Hausdorff Dimension Estimates for Invariant Sets of k — 1 — Endomorphisms

For a special class of non–injective maps on Riemannian manifolds upper and lower bounds for the Hausdorff dimension of invariant sets are given in terms of the singular values of the tangent map. The upper estimation is based on a theorem by Douady and Oesterlé and its generalization to Riemannian manifolds by Noack and Reitmann , but additionally information about the noninjectivity is used. The lower estimation can be reached by modifying a method, derived by Shereshevskij for geometric constructions on the real line (also described by Barreira , for similar constructions in general metric spaces. The upper and lower dimension estimates for k — 1 — endomorphisms can for instance be applied to Julia sets of quadratic maps on the complex plane.