  In this paper, we present a noncommutative scheme theory for the semi-graded
rings generated in degree one defined by Lezama and Latorre
\cite{LezamaLatorre2017} following the ideas about schematicness introduced by
Van Oystaeyen and Willaert \cite{VanOystaeyenWillaert1995} for
$\mathbb{N}$-graded algebras. With this theory, we prove the
Serre-Artin-Zhang-Verevkin theorem \cite{ArtinZhang1994, EGAII1961,
Hartshorne1977, Serre1955, Verevkin1992a, Verevkin1992} for several families of
non-$\mathbb{N}$-graded algebras and finitely non-$\mathbb{N}$-graded algebras
appearing in ring theory and noncommutative algebraic geometry. Our treatment
contributes to the research on this theorem presented by Lezama
\cite{Lezama2021, LezamaLatorre2017} from a different point of view.
