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This is not to diminish Wells's insight: a mathematical formalization of dimension theory was first published by Karl Menger in 1928, and Hurewicz and Wallman's Dimension Theory was published in 1941.
In his treatment of affine algebras and Noetherian rings he describes the Galois theory of fields, algebras and affine fields, transcendence degree and the Krull dimension of a ring, modules and rings satisfying chain conditions, localization in the prime spectrum, the Krull dimension theory of commutative Noetherian rings.