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On the ring of D-valued R-polynomials over E
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2021-01-20 , DOI: 10.1142/s0219498822500876
Ali Tamoussit 1
Affiliation  

Let D be an integral domain with quotient field K, R be an overring of D, X be an indeterminate over R and E be a subset of K. We consider the ring of D-valuedR-polynomials onE, denoted by IntR(E,D), formed by the polynomials f R[X] such that f(a) D for each a E, that is, IntR(E,D) := {f R[X] : f(E) D}. In this paper, we study localization properties, local freeness and faithful flatness of IntR(E,D) over various classes of locally essential domains. In particular, we extend some known results to more general settings.

中文翻译:

在 E 上的 D 值 R 多项式环上

D是具有商场的整数域ķ,R超越D,X是一个不确定的结束R成为的一个子集ķ. 我们考虑环D有价值的R- 多项式,表示为诠释R(,D), 由多项式形成F R[X]这样F(一种) D对于每个一种 , 那是,诠释R(,D) = {F R[X] F() D}. 在本文中,我们研究了定位特性、局部自由度和忠实平坦度。诠释R(,D)涵盖各种类型的本地必要领域。特别是,我们将一些已知结果扩展到更一般的设置。
更新日期:2021-01-20
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