Further results on finitely generated projective modules
type: Item
instance of: scholarly article
title: Further results on finitely generated projective modules
zbMATH Open document ID: 1018.16002
publication date: 2003-06-15T00:00:00Z
review text: Let \(p(R)\) be the category of finitely generated projective \(R\)-modules. The author obtains the following results: (1) For any exchange ring \(R\) and any two-sided ideal \(I\) of \(R\), the canonical ring homomorphism from \(R\) to \(R/I\) induces an epimorphic group homomorphism from \(K_0(R)\) to \(K_0(R/I)\), the kernel of which is \(K=\{[P]-[Q]:P,Q\) in \(p(R)\) and \(P=PI\), \(Q=QI\}\), and \(K\) is the subgroup of \(K_0(R)\) generated by the subset \(\{[eR]\) in \(K_0(R):ee=e\) in \(I\}\) in \(K_0(R)\); (2) For any exchange ring \(R\) with primitive factor rings Artinian, there is an order preserving group isomorphism from \((K_0(R),[R])\) to \((G,u)\), where \(G\) is the Abelian group generated by the cone consisting of all the rational functions over the set of all primitive ideals of \(R\).
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 19A49
zbMATH DE Number: 1885822
zbMATH Keywords: exchange rings
zbMATH Keywords: \(K_0\)-groups
zbMATH Keywords: Artinian primitive factor rings
zbMATH Keywords: categories of finitely generated projective modules
zbMATH Keywords: primitive ideals
author: Tongsuo Wu
reviewed by: Tong Wenting
MaRDI profile type: Publication
full work available at URL: s101140000078
OpenAlex ID: W1984217038
cites work: Lifting Idempotents and Exchange Rings
cites work: Extensions of exchange rings
cites work: Finitely generated projective modules over exchange rings
cites work: Q4056148
cites work: On pi-regular rings whose primitive factor rings are Artinian
DOI: 10.1007/S101140000078
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 1885822