 

Vijay Kumar Bhat
Transparent rings and their extensions


Published: 
July 30, 2009

Keywords: 
Automorphism, derivation, Ore extension, quotient ring, transparent ring, Krull dimension 
Subject: 
Primary 16XX; Secondary 16S36, 16N40, 16P40, 16U20. 


Abstract
Skew polynomial rings have invited attention of mathematicians and
various properties of these rings have been discussed. The nature of
ideals (in particular prime ideals, minimal prime ideals, associated
prime ideals), primary decomposition and Krull dimension have been
investigated in certain cases. In this article, we introduce a
notion of primary decomposition of a noncommutative ring. We say
that a Noetherian ring satisfying this type of primary decomposition
is a transparent ring. We then show that if R is a
commutative Noetherian Qalgebra (Q, the field
of rational numbers) and σ is an automorphism of R, then
there exists an integer m ≧ 1 such that the Ore extension
R[x;α,δ] is a transparent ring, where
σ^{m} = α and δ is an αderivation of R
such that α(δ(a)) = δ(α(a)), for all a∈ R.


Author information
School of Mathematics, SMVD University, P/o SMVD University, Katra, J and K, India 182320
vijaykumarbhat2000@yahoo.com

