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环的投射生成元和K_0群(英文)

PROGENERATORS AND K_0-GROUPS OF RINGS
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摘要 设R是含么结合环,Pg(R )是R的所有投射生成元的同构类组成的半群,Gr(Pg<R>)是Pg<R>的Grothendieck群.在本文中我们证明了K_0(R)= Gr(Pg<R>).由此我们得到对任意VBN环(即非IBN环)R,存在环S满足S~2=S并且S具有Aut-Pic性质.最后我们给出了环的一个分类,并且用Pg<R>的周期性对它作了描述. Let R be an associative ring with identity. Denote Pg(R) for the semigroup of isomorphism classes of progenerators of R, and Gr(Pg(R) ) for the Grothendieck group of Pg (R). In this paper we prove that K, (R) = Gr(Pg<R> ). As an application, we obtain that for any VBN (i. e, non IBN) ring R, K, (R) is isomorphic to an ideal of Pg(R). Then we prove that if R is a VBN ring,there exists a ring S such that S^2 = S and S has the Ant-Pic property. Finally, we give a classification of rings and describe them by the periodicity of Pg(R}.
作者 杜雱 宋光天
出处 《数学杂志》 CSCD 2000年第1期71-75,共5页 Journal of Mathematics
关键词 GROTHENDIECK群 投射生成元 K0群 半群 Grothendieck group,progenerator Morita invariant property
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参考文献1

  • 1Xu Yansong,南京大学学报数学半年刊,1985年,2期,216页

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