唯一分解整环R上不可约多项式的若干结构(英文)

Some Structures of Irreducible Polynomials over a Unique Factorization Domain R

英文关键词:unique factorization domain  prime element  nonimplicit congruence  irreducible polynomial.

中文摘要:

      本文在唯一分解整环Ｒ上引入隐含同余和非隐含同余概念．从而获得Ｒ上多项式不可约性的若干结构．一百多年来首次对著名的Ｅｉｓｅｎｓｔｅｉｎ不可约定理作出重要推广

英文摘要:

      In this paper, we give the conception of implicit congruence and nonimplicit congruence in a unique factorization domain R and establish some structures of irreducible polynomials over R . A classical result, Eisenstein′s criterion, is generalized.