  The aim of this paper is to study integer rounding properties of various
systems of linear inequalities to gain insight about the algebraic properties
of Rees algebras of monomial ideals and monomial subrings. We study the
normality and Gorenstein property--as well as the canonical module and the
a-invariant--of Rees algebras and subrings arising from systems with the
integer rounding property. We relate the algebraic properties of Rees algebras
and monomial subrings with integer rounding properties and present a duality
theorem.
