The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 145-158.
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Let be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate . We restrict to the class of prime divisors that dominate and show that if a collection of such prime divisors is taken below a certain “level,” then the intersection is an almost Dedekind domain having the property that every nonzero ideal can be represented uniquely as an irredundant intersection of powers of maximal ideals.
@article{RSMUP_2020__144__145_0, author = {Heinzer, William and Olberding, Bruce}, title = {The ideal theory of intersections of prime divisors dominating a normal {Noetherian} local domain of dimension two}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {145--158}, volume = {144}, year = {2020}, doi = {10.4171/rsmup/62}, mrnumber = {4186452}, zbl = {1472.13006}, language = {en}, url = {http://www.numdam.org/articles/10.4171/rsmup/62/} }
TY - JOUR AU - Heinzer, William AU - Olberding, Bruce TI - The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2020 SP - 145 EP - 158 VL - 144 UR - http://www.numdam.org/articles/10.4171/rsmup/62/ DO - 10.4171/rsmup/62 LA - en ID - RSMUP_2020__144__145_0 ER -
%0 Journal Article %A Heinzer, William %A Olberding, Bruce %T The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two %J Rendiconti del Seminario Matematico della Università di Padova %D 2020 %P 145-158 %V 144 %U http://www.numdam.org/articles/10.4171/rsmup/62/ %R 10.4171/rsmup/62 %G en %F RSMUP_2020__144__145_0
Heinzer, William; Olberding, Bruce. The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 145-158. doi : 10.4171/rsmup/62. http://www.numdam.org/articles/10.4171/rsmup/62/
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