On semi-pseudo-valuation rings and their extensions
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- 作者：V. K. Bhat (1) vijaykumarbhat2000@yahoo.com
- 关键词：Key words and phrases Ore extension ; automorphism ; derivation ; divided prime ; pseudo ; valuation ring ; near ; pseudo ; valuation ring ; semi ; pseudo ; valuation ring
- 刊名：Lobachevskii Journal of Mathematics
- 出版时间：January 2010
- 出版年：2010
- 期刊代码：pc598_1995-0802
- 类别：mat
- 卷：31
- 期：1
- 页码：8-12
- 数据来源：sp
摘要
Recall that a commutative ring R is said to be a pseudo-valuation ring (PVR) if every prime ideal of R is strongly prime. We say that a commutative Noetherian ring R is semi-pseudo-valuation ring if assassinator of every right ideal (which is uniform as a right R-module) is a strongly prime ideal. We also recall that a prime ideal P of a ring R is said to be divided if it is comparable (under inclusion) to every ideal of R. A ring R is called a divided ring if every prime ideal of R is divided. Let R be a commutative ring, σ an automorphism of R and δ a σ-derivation of R. We say that a prime ideal P of R is δ-divided if it is comparable (under inclusion) to every σ-stable and δ-invariant ideal I of R. A ring R is called a δ-divided ring if every prime ideal of R is δ-divided. We say that a Noetherian ring R is semi-δ-divided ring if assassinator of every right ideal (which is uniform as a right R-module) is δ-divided. Let R be a ring and σ an endomorphism of R. Recall that R is said to be a σ(*)-ring if aσ(a) ∈ P(R) implies that a ∈ P(R), where P(R) is the prime radical of R. With this we prove the following