  In this paper we extend the well-known iterated mapping cone procedure to
monomial ideals in strongly Koszul algebras. We study properties of ideals
generated by monomials in commutative Koszul algebras and show that the linear
strand of ideals generated by linear forms is obtained as a subcomplex of the
Priddy complex. In the case of strongly Koszul algebras, this shows that the
minimal free resolution of a monomial ideal admitting linear quotients is
obtained as an iterated mapping cone, immediately extending results for such
ideals in polynomial rings to strongly Koszul algebras. We then consider
monomial ideals admitting a so-called regular ordering, a generalization of
regular decomposition functions, and show that the comparison maps in the
iterated mapping cone construction can be computed explicitly. In particular,
this gives a closed form for the minimal free resolution of monomial ideals
admitting a regular ordering over strongly Koszul algebras.
