  In a 1987 paper, Eliahou and Kervaire constructed a minimal resolution of a
class of monomial ideals in a polynomial ring, called stable ideals. As a
consequence of their construction they deduced several homological properties
of stable ideals. Furthermore they showed that this resolution admits an
associative, graded commutative product that satisfies the Leibniz rule. In
this paper we show that their construction can be extended to stable ideals in
skew polynomial rings. As a consequence we show that the homological properties
of stable ideals proved by Eliahou and Kervaire hold also for stable ideals in
skew polynomial rings. Finally we show that the resolution we construct admits
a product generalizing the one given by Eliahou and Kervaire in the commutative
case.
