A cancellation theorem for projective modules over affine algebras over C1-fields

✍ Scribed by S.M. Bhatwadekar

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 154 KB
• Volume: 183
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(03)00038-0

✦ Synopsis

Let k be a C1-ÿeld of characteristic zero. Let A be an a ne algebra of dimension d ¿ 2 over k. In this set up, Suslin proved that the free module A d is cancellative (in other words, stably free A-modules of rank d are free). In this note we show that, in fact, all ÿnitely generated projective A-modules of rank d are cancellative.