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## Colloquium Mathematicum

2013 | 130 | 1 | 1-17
Tytuł artykułu

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

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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.
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Rocznik
Tom
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1-17
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wydano
2013
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autor
• Department of Mathematics, Gebze Institute of Technology, Gebze, Kocaeli, Turkey
autor
• Department of Mathematics, National Taiwan University, Taipei 106, Taiwan, Member of Mathematics Division (Taipei Office), National Center for Theoretical Sciences
autor
• Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada
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