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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 Thesis (Masters) Philippoussis, Anthony v, 41 leaves ; 29 cm. Concordia University Theses (M.Sc.) Mathematics and Statistics 1998 Raphael, Robert 484 Concordia University Libraries 27 Aug 2009 17:12 08 Dec 2010 15:14 http://clues.concordia.ca/search/c?SEARC...
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