Existence of unimodular elements in a projective module
نویسندگان
چکیده
منابع مشابه
Unimodular Elements and Projective Modules
We are mainly concerned with the completablity of unimodular rows to an invertible matrix. We first relate this to stable range of the ring. Further, we consider rows generating an idempotent of the ring to obtain completability under special conditions. We try to obtain analogues of important theorems regarding unimodular rows in the case of these “idempotent rows”. By ring, we shall always me...
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Let A be a commutative noetherian ring of dimension n. Let P be a projective A[T ]-module. Plumstead ([P]) proved that if rankP > dimA then P splits off a free summand of rank one. It is natural to ask what happens when rankP = dimA. In this paper we investigate this question when P has trivial determinant. Let α : P I be a generic surjection (i.e. I ⊂ A[T ] is an ideal of height n). It is prov...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2017
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2017.01.009