形式幂级数环

In chapter 4, we define the notions of μ-semirings and λ-semirings and also study the primary properties of them. Moreover, we discuss the interrelation between them and the formal power series semirings of them.

第四章给出了μ-半环和λ-半环的定义和基本性质，讨论了两者的一些内在关系并研究了它们的形式幂级数半环。

The third chapter introduces the notion of inductive *-semirings and weak inductive *-semirings. We give some basic properties of them and discuss the formal power series semirings.

第三章以归纳*-半环为重点，介绍了归纳*-半环及弱归纳*-半环的概念及基本性质，并讨论了归纳*-半环的形式幂级数半环。

In chapter 5, we define the notions of *-μ-semirings as well as *-λ-semirings and also study the primary properties of them. We discuss the interrelation between *-μ-semirings and *-λ-semirings, and their relation with those semirings introduced above. In the end, we study the formal power series semirings of *-λ-semirings as well as weak inductive *-semirings.

第五章给出了*-μ-半环和*-λ-半环的定义和基本性质，讨论了这两类半环之间以及它们与归纳*-半环、弱归纳*-半环之间的一些内在关系并研究了它们的形式幂级数半环。

In this thesis, we define the notions of μ-semirings, A-semirings,*-μ-semirings and *-λ-semirings which extend the notions of inductive *-semirings. we also study the basic properties of these semirings and discuss the interrelation between them. Also, we discuss whether these semirings are closed for the construction of formal power series via a fixed point-theoretical viewpoint.

本文给出了归纳术*-半环及弱归纳*-半环概念的推广，即μ-半环、λ-半环、*-μ-半环以及*-λ-半环的定义；研究了这些半环的一些基本性质以及它们之间的相互关系；同时结合形式幂级数及不动点理论，讨论了这些半环关于形式幂级数构造的封闭性问题。

The theory of rings is an important content of Modern Algebra, while the polynomial rings is an important part of the rings. Polynomial ring is similar with power series ring, and it is a subset of the power series.

摘要环论是近世代数中的重要内容，而多项式环的性质又是环论理论中的重要组成部分，多项式环是幂级数环的子环且与幂级数环形式相近。

A general ring I is a clean general ring if and only if its power series ring is a clean general ring if and only if its skew power series ring is a clean general ring.

1一般环I是一般clean环当且仅当I的形式幂级数环是一般clean环当且仅当I的斜幂级数环是一般clean环。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。