Stably free modules over virtually free groups
نویسندگان
چکیده
منابع مشابه
Stably Free Modules
Let R be a commutative ring. When an R-module has a particular module-theoretic property after direct summing it with a finite free module, it is said to have the property stably. For example, R-modules M and N are stably isomorphic if Rk ⊕M ∼= Rk ⊕N for some k ≥ 0. An R-module M is stably free if it is stably isomorphic to a free module: Rk ⊕M is free for some k. When M is finitely generated a...
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We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre’s problem, was extensively studied befo...
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Let G be a finitely generated virtually-free group. We consider the Birget-Rhodes expansion of G, which yields an inverse monoid and which is denoted by IM(G) in the following. We show that for a finite idempotent presentation P , the word problem of a quotient monoid IM(G)/P can be solved in linear time on a RAM. The uniform word problem, where G and the presentation P are also part of the inp...
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We prove that for any finite-dimensional ringR and n ≥ dimR+2, the group En(R[X]) acts transitively on Umn(R[X]). In particular, we obtain that for any finite-dimensional ringR, all finitely generated stably free modules over R[X] of rank > dimR are free. This result was only known for Noetherian rings. The proof we give is short, simple, and constructive.
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We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2012
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-012-0432-9