Department of Mathematics
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Let R ⊂ S be noetherian algebras over a field k, and assume that SR is finitely generated. A prime ideal Q of S is said to lie over the prime ideal P of R (and P is said to have lying over) if P is minimal among the prime ideals of R that contain Q∩R. A standard prime factor series of a right R-module M is a finite sequence of submodules 0=N₀ ⊂ N₁ ⊂ ⋅⋅⋅ ⊂ N_i ⊂ N_i+1 ⊂ ⋅⋅⋅ ⊂ N_n = M such that for each i the annihilator P_i = r_R(N_i/N_i-1) is the unique associated prime of N_i/N_i-1 and that GKdim(R/P_i) ≤ GKdim(R/P_j) whenever i ≤ j. The talk will explore the connections between the prime ideals of R that have lying over and the prime ideals that arise from standard prime factor series of modules of the form (S/I)R, where I denotes a two-sided ideal of S.