共查询到3条相似文献,搜索用时 0 毫秒
1.
Louis J. Ratliff Jr. 《代数通讯》2013,41(3):1058-1073
2.
3.
William Heinzer 《代数通讯》2013,41(8):3249-3274
Let I be a complete m-primary ideal of a regular local ring (R, m) of dimension d ≥ 2. In the case of dimension two, the beautiful theory developed by Zariski implies that I factors uniquely as a product of powers of simple complete ideals and each of the simple complete factors of I has a unique Rees valuation. In the higher dimensional case, a simple complete ideal of R often has more than one Rees valuation, and a complete m-primary ideal I may have finitely many or infinitely many base points. For the ideals having finitely many base points Lipman proves a unique factorization involving special *-simple complete ideals and possibly negative exponents of the factors. Let T be an infinitely near point to R with dim R = dim T and R/m = T/m T . We prove that the special *-simple complete ideal P RT has a unique Rees valuation if and only if either dim R = 2 or there is no change of direction in the unique finite sequence of local quadratic transformations from R to T. We also examine conditions for a complete ideal to be projectively full. 相似文献