HALF-FACTORIALITY IN SUBRINGS OF TRIGONOMETRIC POLYNOMIAL RINGS - ullah, ehsan (Trends in Computational and Applied Mathematics, 2013)
In this study we explore half-factorial domains in trigonometric polynomial rings. Consider the ring $T^{′ }$ of complex trigonometric polynomials. (see \cite{PP}). We construct the half-factorial domains $T_{2}^{′ },$ $% T_{3}^{′ }$ and $T_{4}^{′ }$ which are the subrings of $T^{′ } $ such that $T_{2}^{′ }\subseteq T_{3}^{′ }\subseteq T_{4}^{′ }\subseteq T^{′ }.$ We also discuss among these subrings 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 $x=x^{′ }x^{′ ′ }.$