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Prime Ideals In Two-Dimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas
Prime Ideals In Two-Dimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas
Department of Mathematics: Dissertations, Theses, and Student Research
This thesis concerns three topics in commutative algebra:
1) The projective line over the integers (Chapter 2),
2) Prime ideals in two-dimensional quotients of mixed power series-polynomial rings (Chapter 3),
3) Fiber products and connected sums of local rings (Chapter 4),
In the first chapter we introduce basic terminology used in this thesis for all three topics.
In the second chapter we consider the partially ordered set (poset) of prime ideals of the projective line Proj(Z[h,k]) over the integers Z, and we interpret this poset as Spec(Z[x]) U Spec(Z[1/x]) with an appropriate identification. …