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Absolute integral closures of commutative rings

Matth\'e van der Lee
Dec 2022
摘要
Absolute integral closures of general commutative unital rings are explored.All rings admit absolute integral closures, but in general they are not unique,as counterexamples demonstrate. Arguments using model theory suggest that anyinfinite connected ring that is not a domain and has "enough zero divisors" hasat least two non-isomorphic absolute integral closures. Universal absoluteintegral closures, which contain every absolute integral closure of a givenring, are shown to exist for certain subrings of products of domains.
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