Slender domains and compact domains

TY - JOUR

T1 - Slender domains and compact domains

AU - Jensen, Chr Ulrik

AU - Jøndrup, Søren

AU - Thorup, Anders

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We prove that a one-dimensional Noetherian domain is slender if and only if it is not a local complete ring. The latter condition for a general Noetherian domain characterizes the domains that are not algebraically compact. For a general Noetherian domain R we prove that R is algebraically compact if and only if R satisfies a condition slightly stronger than not being slender. In addition we enlarge considerably the number of classes of rings for which the question of slenderness can be answered. For instance we prove that any domain, not a field, essentially of finite type over a field is slender.

AB - We prove that a one-dimensional Noetherian domain is slender if and only if it is not a local complete ring. The latter condition for a general Noetherian domain characterizes the domains that are not algebraically compact. For a general Noetherian domain R we prove that R is algebraically compact if and only if R satisfies a condition slightly stronger than not being slender. In addition we enlarge considerably the number of classes of rings for which the question of slenderness can be answered. For instance we prove that any domain, not a field, essentially of finite type over a field is slender.

U2 - 10.1515/forum-2015-0254

DO - 10.1515/forum-2015-0254

M3 - Journal article

SN - 0933-7741

VL - 29

SP - 893

EP - 904

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 4

ER -