EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 86(100), pp. 123–131 (2009)

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FACTORIZATION PROPERTIES OF SUBRINGS
IN TRIGONOMETRIC POLYNOMIAL RINGS

Tariq Shah and Ehsan Ullah

Department of Mathematics, Quaid-I-Azam 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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