ISSN:0092-7872    

DOI:10.1080/00927879508825335

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

Given a finitely generated algebra A and a natural number d, we describe explicitely a decomposition of the variety of all d-dimensional A-modules into finitely many locally closed Gld- stable subvarieties and we give on each of these subvarieties a finite number of Gld-invariant regular functions that separate the orbits. Unfortunately this decomposition is very hard to compute

ISSN:0092-7872    

DOI:10.1080/00927879508825336

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879508825337

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

Let n be an integer greater than 1, and let G be a group. A subset {x1, X2, ..., xn} of n elements of G is said to be rewritable if there are distinct permutations π and σ of {1,2, …, n} such thatThe group G is said to have the rewriting property Qnor to be n-rewritable, if every subset of n elements of G is rewritable. The main result of this paper shows that the only nontrivial semlsimple groups with the property Q5are the alternating group A5, the symmetric group S5, the projective special linear group PSL(2, 7) and the projective general linear group PGL(2, 7)

ISSN:0092-7872    

DOI:10.1080/00927879508825338

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879508825339

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

An associative ring R with identity is said to have stable range one if for any a,b∈ R with aR + bR = R, there exists y ∈ R such that a + by is left (equivalently, right) invertible. The main results of this note are Theorem 2: A left or right continuous ring R has stable range one if and only if R is directly finite (i.e xy = 1 implies yx = 1 for all x,y ∈ R), Theorem 6: A left or rightN0o-quasi-continuous exchange ring has stable range one if and only if it is directly finite, and Theorem 12: left or rightN0-quasi-continuous strongly π-regular rings have stable range one. Theorem 6 generalizes a well-known result of Goodearl [10], which says that a directly finite, rightNo-continuous von Neumann regular ring is unit-regular

ISSN:0092-7872    

DOI:10.1080/00927879508825340

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

A ring R is said to be strongly right (left) bounded if every nonzero right (left) ideal contains a nonzero ideal; and R is right bounded if every essential right ideal contains a nonzero ideal. Strongly right bounded rings play a fundamental role in the theory of FPF rings (e.g., a strongly right bounded

ISSN:0092-7872    

DOI:10.1080/00927879508825341

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules. The notion of an induced invariant form is introduced and a setting in described where all invariant forms are induced

ISSN:0092-7872    

DOI:10.1080/00927879508825342

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879508825343

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor

摘要:

We consider maximal left ideals L of the polynomial ring R[λ1, …, λn], for R noncommutative. In §1 we reprove and generalize Resco's result that any maximal left idealLis generated by ≤ n elements whenever R is simple Artinian, and obtain more precise information about the generators when R satisfies a PI. In many instances, fewer than n generators suffice; this is considered in §3, by means of various examples. In §2 we see by a straightforward argument that L has bounded height as a prime left ideal whenever R is a simple Pl-ring, but this does not- hold in general for R simple Artinian.

ISSN:0092-7872    

DOI:10.1080/00927879508825344

出版商:Marcel Dekker, Inc.    

年代:1995

数据来源: Taylor