二次虚代数整数环中的Euclid整环  

The Euclid Integral Domain in the Quadratic Imaginary Algebraic Integral Domain

作　　者：吴彬[1] 

机构地区：[1]南通职业大学基础部,江苏南通226007

出　　处：《南通职业大学学报》2006年第4期74-75,共2页Journal of Nantong Vocational University

摘　　要：唯一分解是整数环所具有的重要性质,当数系扩充到全体代数整数时,该性质将会消失。该文把整数环扩充到二次虚单纯代数整环,讨论了二次虚单纯代数整环的可既约分解性,进一步探讨了具有Euclid性质的整环,从而得到了二次虚单纯代数整环中能够实现唯一分解的一部分整环。Unique factorization is the important property of the integral domain, but it will be lost when the number system be extended to the total algebraic integers. In this paper, we extends the integral domain to the quadratic imaginary simple algebraic, integral domain, discusses the reductive factorization of which and the integral domain with the Euclid property, and obtains a part of integral domain which can be factorized uniquely in the quadratic imaginary simple algebraic integral domain.

关 键 词：唯一分解 二次虚单纯代数整环 Euclid整环 单一分解整环 

分 类 号：O15[理学—数学]