Difference Algebra, Volume 17

4-series a₁ algebraic extension algebraically closed algebraically independent set algebraically irreducible difference annul b₁ Chapter characteristic set coefficients compatible component of M(P contains defined denote difference field extension difference overfield differential algebra disjoint effective order essential prime divisors exists extension of F field of F follows from Theorem Hence implies integer inversive closure inversive difference field irreducible component irreducible difference polynomial irreducible polynomial irreducible variety isomorphism kernel Lemma linear linearly disjoint low weight condition M₁ monadic extension morphism n-tuple nomial normal closure obtained overfield of F P₁ perfect difference ideal polynomial difference ring polynomial ring prime difference ideal prime ideal principal component principal realization reflexive prime difference replaced result Ritt set of parameters singular component solution subextension subindexing subset term Theorem VIII transformal transcendence transformally transcendental transforming operator underlying field y₁ zero