An intermediate ring between a polynomial ring and a power series ring

• Autorzy: M. Tamer Koşan , Tsiu-Kwen Lee , Yiqiang Zhou
• Języki publikacji: EN

Abstrakty

EN

Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]:
[R;I][x]: = {$∑_{i≥0} r_i x^i ∈ R[[x]]$ : ∃ 0 ≤ n∈ ℤ such that $r_i∈ I$, ∀ i ≥ n}.
The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with a certain ring property suggest a similar study to be carried out for the ring [R;I][x]. In this paper, we characterize when the ring [R;I][x] is semipotent, left Noetherian, left quasi-duo, principal left ideal, quasi-Baer, or left p.q.-Baer. New examples of these rings can be given by specializing to some particular ideals I, and some known results on polynomial rings and power series rings are corollaries of our formulations upon letting I = 0 or R.

Kategorie tematyczne

• 16P40: Noetherian rings and modules
• 16S36: Ordinary and skew polynomial rings and semigroup rings
• 16S34: Group rings , Laurent polynomial rings
• 16W60: Valuations, completions, formal power series and related constructions
• 16E50: von Neumann regular rings and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 130
• Numer: 1
• Strony: 1-17

Daty

wydano

2013

Twórcy

autor

M. Tamer Koşan

• Department of Mathematics, Gebze Institute of Technology, Gebze, Kocaeli, Turkey

autor

Tsiu-Kwen Lee

• Department of Mathematics, National Taiwan University, Taipei 106, Taiwan, Member of Mathematics Division (Taipei Office), National Center for Theoretical Sciences

autor

Yiqiang Zhou

• Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

Identyfikatory

DOI

10.4064/cm130-1-1