论文标题
$ \ bbb z_2 $的均匀频谱
The homogeneous spectrum of a $\Bbb Z_2$-graded commutative ring
论文作者
论文摘要
令$ \ bbb z_2：= \ bbb z/2 \ bbb z $为具有两个元素的加性组。在本文中，我们仅专注于$ \ bbb z_2 $ - 授予的交换戒指，即交换性戒指$ r $，这样$ r = r_0 \ oplus r_1 $作为Abelian Group和$ R_IR_JJ \ subseteq r_ {I in \ in \ in \ in \ in \ bbb z__2 $。我们的主要目标是在$ \ bbb z_2 $ priper（最大）$ r $的理想和prime（最大）理想$ r_0 $之间建立牢固的关系。
Let $\Bbb Z_2:=\Bbb Z/2\Bbb Z$ be the additive group with two elements. In this article, we focus only on $\Bbb Z_2$-graded commutative ring i.e commutative ring $R$ such that $R=R_0\oplus R_1$ as Abelian group and $R_iR_j\subseteq R_{i+j}$ for all $i,j\in \Bbb Z_2$. Our main goals is to establish a strong relation between $\Bbb Z_2$-graded prime ( maximal ) ideals of $R$ and prime ( maximal) ideals of $R_0$, for instance, it is showed that, the $\Bbb Z_2$-graded spectrum of $R$ is homeomorphic to the spectrum of $R_0$ with respect to the Zariski topologies.
