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arXiv · 1807.06396

Decomposition and classification of length functions

Dario Spirito
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Abstract

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 Pr\"ufer 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.

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Dario Spirito. 2018-07-17. Decomposition and classification of length functions. https://arxiv.org/abs/1807.06396

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