Rings graded by polycyclic-by-finite groups
نویسندگان
چکیده
منابع مشابه
Algorithms for Polycyclic-by-finite Groups Algorithms for Polycyclic-by-finite Groups Table of Contents
OF THE DISSERTATION Algorithms for Polycyclic-by-Finite Groups by Gretchen Ostheimer Dissertation Director: Professor Charles C. Sims Let R be a number eld. We present several algorithms for working with polycyclicbynite subgroups of GL(n;R). Let G be a subgroup of GL(n;R) given by a nite generating set of matrices. We describe an algorithm for deciding whether or not G is polycyclic-bynite. Fo...
متن کاملAutomorphism groups of polycyclic-by-finite groups and arithmetic groups
We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construc...
متن کاملAlgorithms for polycyclic-by-finite matrix groups
Let K be a number eld. We present several algorithms for working with polycyclic-by-nite subgroups of GL(n; K). Let G be a subgroup of GL(n; K) given by a nite generatingset of matrices. We describe an algorithm for deciding whether or not G is polycyclic-by-nite. For polycyclic-by-nite G, we describe an algorithm for deciding whether or not a given matrix is an element of G. We also describe a...
متن کاملGraded Cohen-macaulayness for Commutative Rings Graded by Arbitrary Abelian Groups
We consider a commutative ring R graded by an arbitrary abelian group G, and define the grade of a G-homogeneous ideal I on R in terms of vanishing of C̆ech cohomology. By defining the dimension in terms of chains of homogeneous prime ideals and supposing R satisfies a.c.c. on G-homogeneous ideals and has a unique G-homogeneous maximal ideal, we can define graded versions of the depth of R and C...
متن کاملPrime Ideals in Group Algebras Oe Polycyclic-by-finite Groups
Introduction Group algebras K[G] of poly cyclic-by-finite groups are easily-defined, interesting examples of right and left Noetherian rings. Since prime rings and prime ideals are the basic building blocks in the Goldie theory of Noetherian rings, the determination of the structure of the prime ideals of K[G] is certainly of importance. In a recent fundamental paper [8], Roseblade proved that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1988-0920979-3