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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
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 -valued R -polynomials on E , denoted by Int R ( E , D ) , formed by the polynomials f ∈ R [ X ] such that f ( a ) ∈ D for each a ∈ E , that is, Int R ( E , D ) : = { f ∈ R [ X ] : f ( E ) ⊆ D } . In this paper, we study localization properties, local freeness and faithful flatness of Int R ( 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
让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 和乙 成为的一个子集ķ . 我们考虑环D 有价值的 R - 多项式 乙 ,表示为诠释 R ( 乙 , D ) , 由多项式形成F ∈ R [ X ] 这样F ( 一种 ) ∈ D 对于每个一种 ∈ 乙 , 那是,诠释 R ( 乙 , D ) : = { F ∈ R [ X ] : F ( 乙 ) ⊆ 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 ( 乙 , 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
中文翻译:
在 E 上的 D 值 R 多项式环上
让