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$K$-THEORY OF MONOID ALGEBRAS AND A QUESTION OF GUBELADZE
We show that for any commutative Noetherian regular ring 
$R$ containing 
$\mathbb{Q}$, the map 
$K_{1}(R)\rightarrow K_{1}\left(\frac{R[x_{1},\ldots ,x_{4}]}{(x_{1}x_{2}-x_{3}x_{4})}\right)$ is an isomorphism. This answers a question of Gubeladze. We also compute the higher 
$K$-theory of this monoid algebra. In particular, we show that the above isomorphism does not extend to all higher 
$K$-groups. We give applications to a question of Lindel on the Serre dimension of monoid algebras.
