关于Z[c^(1/2)]环  

On Z[c^(1/2)] Ring

作　　者：姚光同[1] 贾璐[1] 

机构地区：[1]山东工商学院数学与信息科学学院,山东烟台264005

出　　处：《黑龙江大学自然科学学报》2004年第3期37-39,共3页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教委自然科学基金;山东工商学院校重点项目

摘　　要：给出Z[c_(1/2)]环的定义,并定义Z[c_(1/2)]环上的元素范数;讨论Z[c_(1/2)]环关于任意主理想的商环的个数,进而得到Z[c_(1/2)]中主理想是极大理想的充要条件,特别在Z[c_(1/2)]是主理想整环的条件下,得到了Z[c_(1/2)]的元素是素元的充要条件。The Z[c^(1/2)] ring is defined, and further, the definition of the norm of any element in Z[c^(1/2)] is provided. The number of quotient rings of Z[c^(1/2)] associated with any principal ideal is discussed. Thereby, a necessary and sufficient condition under which a principal ideal of Z[c^(1/2)] is maximal are obtained. In particular, when Z[c^(1/2)] is a principal ideal domain, a necessary and sufficient condition under which an element of Z[c^(1/2)] is prime is proved.

关 键 词：商环 主理想 极大理想 素元 

分 类 号：O152.5[理学—数学]