关于多项式的同余与剩余类环

关于多项式的同余与剩余类环

摘  要: 本文介绍了1元及2元多项式剩余类环的概念，并将数论的研究方法推广到多项式的同余中，详细地讨论了多项式剩余类环的结构，环中的元素可分两类：1类为可逆元，另1类为0因子；并提出了多项式环中的元是乘法可逆元的充要条件以及该环非域时环中可逆元与0因子的判别法．
关键词：同余；多元多项式；剩余类环

On the Congruence and Residue Class Ring of Polynomials

Abstract: In this paper the concept of modulus multivariate polynomial residue class rings has been set up，the method to study number theory is used, the composition of polynomial residue class rings is discussed in detail. There are two kinds of elements in the rings. One is reversible element, and the other is zero divisor. The necessary and sufficient condition for polynomial ring can be multiplication reversible element and the judgment for reversible elements and zero divisors when the rings are not fields are also discussed.  
Keywords: Congruence; multivariate polynomial; residue class ring.