分次环的分次奇异性的一点注记

A NOTE FOR GRADED NONSINGULAR PROPERTY OF A GRADED RING

设Ｇ是有序群，Ｒ是Ｇ－分次环，则Ｚ（Ｒ）＾￣＝Ｚ（Ｒ）￣＝ＺＧ（Ｒ）＝Ｚ（Ｒ），ＺＧ（Ｒ）分别表示Ｒ的奇异理想和分次奇异理想。

Let G be an ordered group,R a G-graded ring,then Z(R)~~=Z(R)_~=Z_G(R)= Z(R),where Z(R)and Z_G(R)denote the singular ideal and graded singular ideal of a graded ring R respectively.