
Vietnam Journal of Mathematics 36:4(2008)
455461

Ore Extensions over 2primal Rings

V. K. Bhat and Ravi
Raina

Abstract. Let R be a ring, σ an automorphism of R and let δ be a σderivation of R. Recall that a ring R
is said to be a δring if aδ(a) P(R) implies a P(R), where P(R) denotes the
prime radical of R.
It is known that if R is a δNoetherian Qalgebra, σ and δ are as
usual such that σ(δ(a))
= δ(σ(a)), for all a R
and σ(P) = P, for all minimal prime ideals P of R, then R[x, σ, δ] is a 2primal
Noetherian ring. In this article it is proved that in the case δ is the zero map, R is a 2primal Noetherian ring implies that R[x, σ] is a 2primal Noetherian ring. In the case σ is
the identity map, a similar result is proved for the differential operator
ring R[x, δ] (R in this
case is moreover a Noetherian Qalgebra).


1991 Mathematics Subject Classification: Primary 16XX,
Secondary 16N40, 16P40, 16W20, 16W25.

Keywords: 2primal, Minimal prime, prime radical,
nil radical, automorphism, derivation.


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by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013

