An axiomatic closure-operator framework for approximate rings and modules proves that approximate prime ideals are closed and the approximate spectrum is the fixed-point subspace of the classical spectrum.
İnan,Approximately rings in proximal relator spaces, Turkish Journal of Mathematics 43(6):2941–2953, 2019
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Approximate Algebra via Closure Operators: An Axiomatic Theory of Modules and Geometry
An axiomatic closure-operator framework for approximate rings and modules proves that approximate prime ideals are closed and the approximate spectrum is the fixed-point subspace of the classical spectrum.