Dissertation > Excellent graduate degree dissertation topics show

FSF-Modules and Rational Invariants of Special Subgroups of Classical Groups

Author: WangTao
Tutor: TangZhongMing
School: Suzhou University
Course: Basic mathematics
Keywords: a pair of ideals generalized local cohomology FSF module associated prime ideal classical group rational invariant
CLC: O153.3
Type: Master's thesis
Year: 2011
Downloads: 8
Quote: 0
Read: Download Dissertation

Abstract


Local cohomology is an effective tool in studying commutative algebra and algebric geometry. Many scholars have been absorbed in studying it and have made some effort to develop it. In 1974, J. Herzog introduced the notation of generalized local cohomology. Then in 2009, R. Takahashi and others extended it to local cohomology with respect to a pair of ideals. In this paper, we study FSF modules and their properties firstly. In view of these, we abtain some good conclusions:If M is a FSF module and t a non-negative integer such that HIi,J(M) is FSF module for all i< t, then the R-module HomR(R/I,J(M)) is FSF, as a consequence, the associated prime of HIt,J(M) is finite; Let M be a finitely generated projective R-module, N be a R module and t a non-negative integer such that ExtRtM/IM,N) is FSF, then for any FSF submodule U of the first non I - FSF finite module HIt(M,N), the R-module HomR(M/IM,HIt(M,N)/U) is FSF, as a consequence, the set of associated prime of HIt(M, N)/U is finite.All the time, the rational invariant theory absorbed many mathematicians. It affects a lot of mathematical branches and physical domains widely. In 1911. L. E. Dickson gave the rational invariants of GLn (Fq) and SLn(Fq). Recently, the invariants of other classical groups also gained good results. The second part of this paper gives some important conclusions: If G1,G2 are subgroups of classical groups, then rational invariants of their internal direct product are the intersection of their rational invariants; If G1, G2 are subgroups of classical groups, and Fq(T1), Fq(T2) are rational invariants of G1,G2 respectively, then the rational invariants of G1∩G2 are Fq(T1)(T2). Besides,we study the rational invariants of the group∑and SOn(Fq).

Related Dissertations

  1. Generalized Local Cohomology Modules,O154.2
  2. The limited nature of generalized local cohomology mode,O153.3
  3. Relative Homological Dimensions and Their Applications,O153.3
  4. BN-Pairs and Invariants of Special Subgroups of Classical Groups,O152
  5. Modular Invariants of Finite Classical Groups,O152
  6. Poisson algebra on non-commutative number of studies,O153
  7. Weak Hoft nature and weak algebraic invariants Hoft mold research,O153.3
  8. Some Properties of Quasi-C Poset and Generalized Completely Distributive Poset,O153.1
  9. Some Studies About Semirings,O153.3
  10. The Characterization of Generators and Cogenerators in the Category of Semimodules,O153.3
  11. Commutativity of Rings with Constraints on Varying Polynomial Equality,O153.3
  12. Overview of the vertex algebra and mirror symmetry,O153
  13. A Study on Soft Ring Theory,O153.3
  14. The Algorithms of Generating Concept Lattice,O153.1
  15. Properties of Fitting Sets and Injecters of Fitting Sets,O153.3
  16. The Characterization of Congruences on Inverse Semirings,O153.3
  17. Some Properties of Strong Raney Posets and HC-Posets,O153.1
  18. Some Notes on Endomorphism Rings of Quasi AP (AGP)-Injective Modules,O153.3
  19. Derivations and Generalized Derivations in Prime Rings,O153.3
  20. Dialgebras and Associative Algebras,O153

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Ring Theory
© 2012 www.DissertationTopic.Net  Mobile