STABLY FREE MODULES OVER ARE FREE
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...
متن کاملStably free modules over R[X] of rank > dim R are free
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.
متن کاملNon-trivial stably free modules over crossed products
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...
متن کاملSome Stably Free Modules Which Are Not Self Dual
We give some examples of stably free modules which are not self dual.
متن کاملFree Modules over Cartesian Closed Topological Categories
The construction of free R-modules over a cartesian closed topological category X is detailed (where R is a ring object in X), and it is shown that the insertion of generators is an embedding. This result extends the well-known construction of free groups, and more generally of free algebras over a cartesian closed topological category.
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: Mathematika
سال: 2018
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579318000050