中文摘要：

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。

英文摘要：

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.