# IJPAM: Volume 52, No. 5 (2009)

**PRIME RADICAL OF ORE EXTENSIONS OVER -RINGS**

School of Mathematics

Shri Mata Vaishno Devi University (SMVD University)

Katra (J and K), 182320, INDIA

e-mail: vijaykumarbhat2000@yahoo.com

e-mail: rainaravirr@yahoo.co.in

**Abstract.**Let R be a ring. Let be an automorphism of R. We recall the
definition of a -ring, and find a relation between the
prime radical of a -ring R and that of . Let
now be a -derivation of R. We say that a ring R is
a -ring if
implies , ; where P(R) is the prime radical of R. We then find a relation
between the prime radical of a -ring R and that of
. We generalize the result for a Noetherian
Q-algebra (Q is the field of rational numbers).

**Received: **July 26, 2007

**AMS Subject Classification: **

**Key Words and Phrases: **radical, automorphism, derivation, completely prime, -ring, Q-algebra

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 52

**Issue:** 5