Cardinality restrictions on Noetherian spectra
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This thesis is concerned with understanding the prime ideal structure in certain classes of commutative Noetherian rings. We offer, within the realm of two-dimensional partially ordered sets with finitely many maximal nodes of height two, broad classifications as they arise as the spectrum of a Noetherian ring. We also offer a technique for adjoining many elements to a graded ring without disturbing its prime ideal structure.