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arXiv · 2208.04463

The homogeneous spectrum of a $\Bbb Z_2$-graded commutative ring

Mohamed Aqalmoun
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Abstract

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.

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Mohamed Aqalmoun. 2022-08-08. The homogeneous spectrum of a $\Bbb Z_2$-graded commutative ring. https://arxiv.org/abs/2208.04463

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