长度函数的分解与分类
Decomposition and classification of length functions
摘要：
研究了整环上的长度函数的分解，将其分解为由覆盖环构造的长度函数的和。当整环包含一个Jaffard族，当它是Noether域，当它是Prüfer域，使得每个理想只有1000个极小素数时，我们找到了一个标准表示.我们还证明了奇异长度函数和局部化系统之间存在自然的双射对应关系。
英文摘要：
We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length functions and localizing systems.
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。
