Transfer of the GPIT Property in Pullbacks
| Autor: | David E. Dobbs, Jay Shapiro |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/2012/743873 |
| Popis: | Let 𝑇 be a commutative ring, 𝐼 a prime ideal of 𝑇, 𝐷 a subring of 𝑇/𝐼, and 𝑅 the pullback 𝑇×𝑇/𝐼𝐷. Ascent and descent results are given for the transfer of the 𝑛-PIT and GPIT (generalized principal ideal theorem) properties between 𝑇 and 𝑅. As a consequence, it follows that if 𝐼 is a maximal ideal of both 𝑇 and 𝑅, then 𝑅 satisfies 𝑛-PIT (resp., GPIT) if and only if 𝑇 satisfies 𝑛-PIT (resp., GPIT). |
| Databáze: | Directory of Open Access Journals |
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