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A note on Itoh (e)-Valuation Rings of and Ideal
[article]
2016
arXiv
pre-print
Let I be a regular proper ideal in a Noetherian ring R, let e > 2 be an integer, let T_e = R[u,tI,u^1/e]' ∩ R[u^1/e,t^1/e] (where t is an indeterminate and u =1/t), and let r_e = u^1/e T_e. Then the Itoh (e)-valuation rings of I are the rings ( T_e/z)_(p/z), where p varies over the (height one) associated prime ideals of r_e and z is the (unique) minimal prime ideal in T_e that is contained in p. We show, among other things: (1) r_e is a radical ideal if and only if e is a common multiple of
arXiv:1607.05341v1
fatcat:ziswfv4g5vff7nehuvgyymcuq4