【摘要】 将上述论文中之某些结论予以推广。1)设R为一有赋值v的环,v的核是R中一极大理理想φ。于是(R,v)成为完全赋值环,当且仅当(F,v)是完全赋值域,此处F=R/p,v是由v所导出。2)设v是环R的一个赋值,其核为R中极大理想;又设S为R的整扩环,且又是R上的有限R-模。于是(1)v在S上有拓展,设为w,它的核是S中一极大理想(2)(S,w)是个完全赋值环。3)前文定理4中关于S的条件可简化为:S是R的一个整扩张,且为R上的有限R-模。更多还原

【Abstract】 Here we generalize several results of the quoted paper.1)let Rbe a ring with valuation v whose core is a maximal ideal pin R.Then(R,v)is complete if and only if the related valued field(F,v)is complete,where F=R/p,vis induced by v.2)Let vbe a valuation of the ring R with maximal ioeal as its core;and let Sbe an integral extension of R,and also a finite R-module over R.Then.(1)v has prolongation to S,say w,whose core is a maximal ideal in S.(2)(S,w)is a complete valued ring.3)Conditions on Sin Theorem 4of the quoted paper can be simplified as follows:S is an integral extension of R,and also a finite R-module over R.更多还原