微分常数与微分理想
Constants of Differentiation and Differential Ideals
摘要：
设R是一个微分域，它在一个微分域F上生成，F的常数域C的特征为0。设E是R的商域。本文研究了R的微分理想使E的微分常数也为C（无新常数）的充要条件.众所周知，没有真的非零微分理想保证没有新的常数。本文证明了当C是代数闭的时，如果R只有n个高度为1的素微分理想，则E将没有新的常数.一个F在C上无限生成的例子表明，相反的情况是错误的。本文给出了C和F上的条件，使得当F是C上的多项式生成环且R是F上的多项式环时，E中没有新的常数意味着R只有有限多个高度为1的素微分理想.
英文摘要：
Let R be a differential domain finitely generated over a differential field, F, with field of constants, C, of characteristic 0. Let E be the quotient field of R. The paper investigates necessary and sufficient conditions on R's differential ideals for the constants of differentiation of E to also be C (no new constants). It was known that no proper nonzero differential ideals guarantees no new constants. The paper shows that when C is algebraically closed that if R has only finitely many height one prime differential ideals that E will have no new constants. An example with F infinitely generated over C shows the converse is false. The paper gives conditions on C and F so that when F is finitely generated over C and R is a polynomial ring over F that no new constants in E implies that R has only fintely many height one prime differential ideals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
