Efficient generation of ideals in a discrete Hodge algebra
  Let $R$ be a commutative Noetherian ring and $D$ be a discrete Hodge algebra over $R$ of dimension $d>\text{dim}(R)$. Then we show that   (i) the top Euler class group $E^d(D)$ of $D$ is trivial.   (ii) if $d>\text{dim}(R)+1$, then $(d-1)$-st Euler class group $E^{d-1}(D)$ of $D$ is trivial. 
Manoj K. Keshari and Md. Ali Zinna
math.AC