Various properties of a general class of integer-valued polynomials

被引：2

作者：

Chems-Eddin, Mohamed Mahmoud ^{[1
]}

Tamoussit, Ali ^{[2
]}

机构：

[1] Univ Sidi Mohamed Ben Abdallah, Fac Sci Dhar El Mahraz, Dept Math, Fes, Morocco

[2] Reg Ctr Educ & Training Profess Souss Massa, Dept Math, Inezgane, Morocco

来源：

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2023年 / 64卷 / 01期

关键词：

Integer-valued polynomials; Localization; Prime ideals; (Faithfully) flat modules; Krull dimension; RINGS; OVERRINGS; DOMAINS; IDEALS;

D O I：

10.1007/s13366-021-00619-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study various properties for some classes of domains that are generalizations of integer-valued polynomial rings. For D an integral domain with quotient field K and E a subset of K, one defines as usual Int (E, D) := {f is an element of K[X] : f(E) subset of D}. If R is an integral domain containing D, then we define Int(R) (E, D) := {f is an element of R[X] : f(E) subset of D}, which is called the ring of D-valued R-polynomials over E. Among other things, we investigate various properties and facts around the rings Int(R) (E, D), such as localization, (faithful) flatness, Krull dimension and some other transfer properties.

引用

页码：81 / 93

页数：13