Submission date: 13 December 2022

Abstract:

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 any infinite connected ring that is not a domain and has “enough zero divisors” has at least two non-isomorphic absolute integral closures. Universal absolute integral closures, which contain every absolute integral closure of a given ring, are shown to exist for certain subrings of products of domains.

Mathematics Subject Classification: 13B02, 13B21, 13M99

Keywords and phrases:

Full text arXiv 2212.06738: pdf, ps.