  A well-known conjecture says that every one-relator group is coherent. We
state and partly prove an analogous statement for graded associative algebras.
In particular, we show that every Gorenstein algebra $A$ of global dimension 2
is graded coherent.
  This allows us to define a noncommutative analogue of the projective line
$\PP^1$ as a noncommutative scheme based on the coherent noncommutative
spectrum $\cohp A$ of such an algebra $A$, that is, the category of coherent
$A$-modules modulo the torsion ones. This category is always abelian Ext-finite
hereditary with Serre duality, like the category of coherent sheaves on
$\PP^1$. In this way, we obtain a sequence $\PP^1_n $ ($n\ge 2$) of pairwise
non-isomorphic noncommutative schemes which generalize the scheme $\PP^1 =
\PP^1_2$.
