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 x ∈ B there exist x ∈ U (B) and x" ∈ A such that x = x'x", where U (B) denote the group of units of B.
trigonometric polynomial; HFD; condition 1; condition 2; irreducible
