Transfer of the GPIT Property in Pullbacks

David E. Dobbs and Jay Shapiro

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-6

Abstract:

Let 𠑇 be a commutative ring, ð ¼ a prime ideal of 𠑇 , ð · a subring of 𠑇 / ð ¼ , and ð ‘… the pullback 𠑇 × 𠑇 / ð ¼ ð · . Ascent and descent results are given for the transfer of the ð ‘› -PIT and GPIT (generalized principal ideal theorem) properties between 𠑇 and ð ‘… . As a consequence, it follows that if ð ¼ is a maximal ideal of both 𠑇 and ð ‘… , then ð ‘… satisfies ð ‘› -PIT (resp., GPIT) if and only if 𠑇 satisfies ð ‘› -PIT (resp., GPIT).

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:743873

DOI: 10.1155/2012/743873

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