Dp-Minimal integral domains
نویسندگان
چکیده
It is shown that every dp-minimal integral domain R a local ring and for non-maximal prime ideal ℘ of R, the localization R℘ valuation ℘R℘ = ℘. Furthermore, if only its residue field infinite or finite maximal principal.
منابع مشابه
Dp-Minimal Valued Fields
We show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.
متن کاملOn dp-minimal ordered structures
We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal.
متن کاملOf Integral Domains
The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-mult...
متن کاملPutting topologies on dp-minimal fields
4. If b ∈ acl(aS), then dp-rk(b/S) ≤ dp-rk(a/S). 5. dp-rk(ab/S) ≤ dp-rk(a/bS) + dp-rk(b/S). We work in a monster model C of a dp-minimal field (i.e., a field of dp-rank 1). “Models” will refer to small elementary substructures M C. We’ll write concatenation multiplicatively and multiplication using ·. We will assume that C is not strongly minimal. One already knows what strongly minimal fields ...
متن کاملTame topology over dp-minimal structures
In this paper we develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous “multi-valued f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2021
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-021-2254-6