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Necessary and sufficient conditions so that a commutative ring can be embedded into a strongly pi-regular ring

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Necessary and sufficient conditions so that a commutative ring can be embedded into a strongly pi-regular ring

Philippoussis, Anthony (1998) Necessary and sufficient conditions so that a commutative ring can be embedded into a strongly pi-regular ring. Masters thesis, Concordia University.

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Abstract

If R is commutative ring then R can be embedded into a strongly $\pi$-regular ring if and only if there exists a set of prime ideals Y = $\{$P$\sb\alpha\}\alpha\in\Lambda$ and for each P$\sb\alpha$, a P$\sb\alpha$-primary ideal Q$\sb\alpha$ such that: (I) Y is closed in the patch topology on Spec R. (II) $\rm\cap\sb{\alpha\in\Lambda}Q\sb\alpha=\{0\}$. (III) for each a $\in$ R there is n(a) $\in$ N such that for n $\ge$ n(a), $\rm\{P\sb\alpha\mid P\sb\alpha\in Y$ and $\rm a\sp{n}\in Q\sb\alpha\}$ is patch open in Y.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Philippoussis, Anthony
Pagination:v, 41 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Mathematics and Statistics
Date:1998
Thesis Supervisor(s):Raphael, Robert
ID Code:484
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:12
Last Modified:08 Dec 2010 10:14
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