Half-factoriality in subrings of trigonometric polynomial rings

Abstract

Trigonometric polynomials are widely used in different fields of engineering and science. Inspired by their applications, we investigate half-factorial domains in trigonometric polynomial rings. We construct the half-factorial domains T '2, T'3 and T'4 which are the subrings of the ring of complex trigonometric polynomials T , such that T'2 ⊆ T'3 ⊆ T'4 ⊆ T'. We also discuss among these three subrings the Condition: Let A ⊆ B be a unitary (commutative) ring extension. For each ∈ B there exist ∈ U (B) and x ∈ A such that = x'x, where U (B) denote the group of units of B.