Abstract
Prime and maximal ideals play a central role in the general theory of commutative rings. This paper contains an exposition of some known results concerning prime and maximal ideals of a commutative monoid ring T. Topics covered include the (Krull) dimension of T, conditions on chains of prime ideals of T, the existence of only finitely many maximal or prime ideals of T, and conditions under which T is a Dedekind domain, a general ZPI-ring, or a Hilbert ring.
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