  Let $R$ be a commutative Noetherian ring of dimension $d$. In 1973, Eisenbud
and Evans proposed three conjectures on the polynomial ring $R[T]$. These
conjectures were settled in the affirmative by Sathaye, Mohan Kumar and
Plumstead. One of the primary objectives of this article is to investigate the
validity of these conjectures over Noetherian subrings of $R[T]$ of dimension
$d+1$, containing $R$. We formulate a class of such rings, which includes
polynomial rings, Rees algebras, Rees-like algebras and Noetherian symbolic
Rees algebras, and exhibit that all three conjectures hold for rings belonging
to this class.
