Indivisible Sequences and Descendability
Ivan Zelich

TL;DR
This paper introduces indivisible sequences and demonstrates that certain faithfully flat ring maps associated with them can be non-descendable, providing new examples in the context of ring theory.
Contribution
It establishes a novel connection between indivisible sequences and the existence of non-descendable faithfully flat ring maps, including the first such examples between certain countable rings.
Findings
Existence of non-descendable faithfully flat ring maps from indivisible sequences.
First example of a faithfully flat ring map between l_{n-1}-countable rings with a specific descendability exponent.
Counterexamples involving l_{\u221e}-countable rings that are not descendable.
Abstract
We introduce the notion of indivisible sequences and show that to any indivisible sequence we can associate faithfully flat ring maps that are not descendable. As a corollary, we obtain the first example of a faithfully flat ring map between -countable rings that has descendability exponent , and indeed a faithfully flat ring map between -countable rings that is not descendable.
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Taxonomy
TopicsCellular Automata and Applications · Computability, Logic, AI Algorithms
