【摘要】 对有乘法单位元的交换环上的非精简显赋值定义一种"完全性"。首先就Von Neumann正则环成为完全赋值环给出一个充分必要条件(定理1);并对正则的完全赋值环证明在它的代数扩环上也能给出完全的拓展赋值(定理2)。其次,再对另一种特殊的环给出与定理1和定理2相同的结论(定理3,4)。更多还原

【Abstract】 In the following all rings appeared will be commutative with identity.At first,a definition of"Completeness"for valued-rings is given.Now let R be a von Neumann regular ring with a nontrivial valuation v,a necessary and sufficient condition that(R,v)be complete is given(Theorem i).Let(S,w)be an algebraic excension of a complete valued-ring(R,v)then(S,w)is also complete(Theorem 2).As for rings having only a finite number of idealso similar results can als be established(Theorems 3,4).更多还原