从多项式环到幂级数环的推广

 从多项式环到幂级数环的推广

摘要

众所周知，幂级数环是多项式环的推广，有许多性质与多项式环相类似．本文主要通过对多项式环的性质以及多项式剩余类环的平坦性的研究，进而研究幂级数环的性质以及幂级数剩余类环的平坦性．即本文主要运用类比的方法把多项式环的1些性质推广到幂级数环上．如：定理4.1，定理4.2，定理4.3，定理4.4．同时把多项式剩余类环的性质推广到幂级数剩余类环上．如：命题6.1，命题6.2，命题6.3等．

关键词：多项式环；幂级数环；推广；性质；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