【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。更多还原

【Abstract】 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.更多还原