Geodesic
Factorization properties of subrings in trigonometric polynomial rings
Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 123 .

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We explore the subrings in trigonometric polynomial rings and their factorization properties. Consider the ring $S'$ of complex trigonometric polynomials over the field $\mathbb{Q}(i)$ (see \cite{SU}). We construct the subrings $S'_1$, $S'_0$ of $S'$ such that $S'_1\subseteq S'_0\subseteq S'$. Then $S'_1$ is a Euclidean domain, whereas $S'_0$ is a Noetherian HFD. We also characterize the irreducible elements of $S'_1$, $S'_0$ and discuss among these structures the condition: Let $A\subseteq B$ be a unitary (commutative) ring extension. For each $x\in B$ there exist $x'\in U(B)$ and $x''\in A$ such that $x=x'x''$.
DOI : 10.2298/PIM0900123S
Classification : 13A05 13B30 12D05 42A05
Keywords: trigonometric polynomial, HFD, substructures, condition 1, irreducible 
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     title = {Factorization properties of subrings in trigonometric polynomial rings},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {123 },
     publisher = {mathdoc},
     volume = {_N_S_86},
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     year = {2009},
     doi = {10.2298/PIM0900123S},
     zbl = {1221.13001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0900123S/}
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Tariq Shah; Ehsan Ullah. Factorization properties of subrings in trigonometric polynomial rings. Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 123 . doi : 10.2298/PIM0900123S. http://geodesic.mathdoc.fr/articles/10.2298/PIM0900123S/

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