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

Subrings of polynomial rings and the conjectures of Eisenbud and Evans