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Ring extensions and related topics

13B02 Extension theory
13B05 Galois theory 
13B10 Morphisms
13B21 Integral dependence
13B22 Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
13B24 Going up; going down; going between
13B25 Polynomials over commutative rings [See also 11C08, 13F20, 13M10]
13B30 Quotients and localization
13B35 Completion [See also 13J10]
13B40 Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
13B99 None of the above, but in this section