International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 20138, 6 pages
Polynomial Rings over Pseudovaluation Rings
School of Applied Physics and Mathematics, Shri Mata Vaishno Devi University, P/o Kakryal, Katra, 182301, India
Received 5 March 2007; Accepted 1 August 2007
Academic Editor: Howard E. Bell
Copyright © 2007 V. K. Bhat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
be a ring. Let be an automorphism of . We define a
-divided ring and prove the following.
(1) Let be a commutative pseudovaluation ring such that for any
. Then is also a pseudovaluation ring.
(2) Let be a -divided ring such that for any
Then is also a -divided ring.
Let now be a commutative Noetherian -algebra ( is the field of rational
numbers). Let be a derivation of . Then we prove the following.
(1) Let be a commutative pseudovaluation ring. Then is also a
(2) Let be a divided ring. Then is also a divided ring.