本文讨论赋值环上的对称线性型、二次型和对称矩阵的合同标准形。
In this paper we will discuss symmetric bilinear forms and quadratic forms over valuation rings, and establish the congruent standard forms of symmetric matrices over valuation rings.
第一章中，我们研究了剩余域是代数闭域的离散赋值环上的完全分次代数；
In the first chapter, we discuss the fully graded algebras over discrete valuation ring with an algebraically closed residue field of characteristic p.
本文给出了有单位元的弱准素环的一个新刻划并给出了弱准素整环是拟赋值环或赋值环的条件。
We give a new characterization of weakly primary rings with identity and conditions that a weakly primary domain is a valuation ring or quasi-valuation ring.
在有单位元的交换环上，引入了M-赋值与序之间的相容性，由此获得一些有关M-赋值与序相容的结果。
The compatibility between M-valuations and orderings is introduced on a commutative rings with unit, and several results on the compatibihty between M-valuations and orderings are established.
在带有单位元的交换环上，引入了V-赋值与亚序间的相容性，并得出了一些性质。
This paper introduces the notion of compatibility between preorderings and V-valuations on commutative rings with units and obtain some relevant results.
在本文中，我们引进了M -赋值系统的概念，从环的内部给出交换环上M -赋值的结构。
In this paper, we introduce the notion of M-valuation systems for a commutative ring, and investigate the M-valuations from the inside of a commutative ring.
在本文中，我们引进了M -赋值系统的概念，从环的内部给出交换环上M -赋值的结构。
In this paper, we introduce the notion of M-valuation systems for a commutative ring, and investigate the M-valuations from the inside of a commutative ring.
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