On The Hilbert Basis Theorem Over Skew Polynomial Rings and Skew Power Series Rings

Let R be a unitary ring and α: R R be a ring endomorphism of R . In this note, we will provide another proof of Hilbert basis Theorem for skew polynomial ring R[x;α ] and skew power series ring R[[x;α ]]. Also, we will extend this theorem for rings R[Fn ; α1, α2,..., αn] and R[[Fn ; α1, α2,..., αn ]] such that F be a free monoid and α1,α2,...,αn are ring automorphisms.

کلیدواژه ها:

Noetherian skew Polynomial rings ، Noetherian skew Power series rings ، Hilbert basis Theorem