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FACTORIZATION PROPERTIES OF SUBRINGS
IN TRIGONOMETRIC POLYNOMIAL RINGS
Tariq Shah and Ehsan Ullah
Department of Mathematics, QuaidIAzam University, Islamabad, Pakistan and Fakultät für Informatik und Mathematik, Passau Universität, Passau, Germany
Abstract: 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 $x=x'x"$.
Keywords: trigonometric polynomial, HFD, substructures, condition 1, irreducible
Classification (MSC2000): 13A05, 13B30; 12D05, 42A05
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Electronic fulltext finalized on: 4 Nov 2009.
This page was last modified: 26 Nov 2009.
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