從多項式環(huán)到冪級數環(huán)的推廣

從多項式環(huán)到冪級數環(huán)的推廣

 從多項式環(huán)到冪級數環(huán)的推廣

摘要

眾所周知，冪級數環(huán)是多項式環(huán)的推廣，有許多性質與多項式環(huán)相類似．本文主要通過對多項式環(huán)的性質以及多項式剩余類環(huán)的平坦性的研究，進而研究冪級數環(huán)的性質以及冪級數剩余類環(huán)的平坦性．即本文主要運用類比的方法把多項式環(huán)的1些性質推廣到冪級數環(huán)上．如：定理4.1，定理4.2，定理4.3，定理4.4．同時把多項式剩余類環(huán)的性質推廣到冪級數剩余類環(huán)上．如：命題6.1，命題6.2，命題6.3等．

關鍵詞：多項式環(huán)；冪級數環(huán)；推廣；性質；平坦性

The Generalizations from The Properties of Polynomial Rings to Power Series Rings

ABSTRACT

As everyone knows, the properties of power series rings are similarly to polyrominal rings in many aspects. In this paper we mainly investigated the primarily properities of polynomial rings and power series rings. Morever we obtain the conditions of  and  being flat modules. Then this text mainly used the top of the wreath of the method research of certificate which properties could expand power series wreath. Such as: Theorem 4.1, Theorem 4.2, Theorem 4.3, Theorem 4.4. Popularized from the properties of the surplus ring of the multinomial to the surplus ring of the power series at the same time. Such as: Proposition 6.1, Proposition 6.2, Proposition 6.3 and so on.

Key words: polynomial ring; power series ring; generalize; property; flat modules 

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