On a particular subspace of homogeneous preserving star operations

Abstract

Let $\Gamma$ be a torsionless commutative cancellative monoid, $R={⨁}_{\alpha \in \Gamma }{R}_{\alpha }$ be a $\Gamma$-graded integral domain. In this note we show that each homogeneous star operation $\star :\mathbf{HF}(R)\to \mathbf{HF}(R)$ of $R$, is the restriction of a (classical) star operation $e(\star ):F(R)\to F(R)$ of $R$. We also show that the set $HSta{r}_f(R)$ of homogeneous star operations of finite type on $R$, endowed with the Zariski topology, is a spectral space.

14 pages