  Considering finite extensions K[A] \subseteq K[B] of positive affine
semigroup rings over a field K we have developed in [1] an algorithm to
decompose K[B] as a direct sum of monomial ideals in K[A]. By computing the
regularity of homogeneous semigroup rings from the decomposition we have
confirmed the Eisenbud-Goto conjecture in a range of new cases not tractable by
standard methods. Here we first illustrate this technique and its
implementation in our Macaulay2 package MonomialAlgebras by computing the
decomposition and the regularity step by step for an explicit example. We then
focus on ring-theoretic properties of simplicial semigroup rings. From the
characterizations given in [1] we develop and prove explicit algorithms testing
properties like Buchsbaum, Cohen-Macaulay, Gorenstein, normal, and seminormal,
all of which imply the Eisenbud-Goto conjecture. All algorithms are implemented
in our Macaulay2 package.
