HALF-FACTORIALITY IN SUBRINGS OF TRIGONOMETRIC POLYNOMIAL RINGS

Abstract

In this study we explore half-factorial domains in trigonometric polynomial
rings. Consider the ring $T^{\prime }$ of complex trigonometric polynomials.
(see \cite{PP}). We construct the half-factorial domains $T_{2}^{\prime },$ $%
T_{3}^{\prime }$ and $T_{4}^{\prime }$ which are the subrings of $T^{\prime }
$ such that $T_{2}^{\prime }\subseteq T_{3}^{\prime }\subseteq T_{4}^{\prime
}\subseteq T^{\prime }.$ 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 $x^{\prime }\in U(B)$ and $x^{\prime \prime }\in A$ such
that $x=x^{\prime }x^{\prime \prime }.$