Subrings in Trigonometric Polynomial Rings
نویسندگان
چکیده
In this study we explore the subrings in trigonometric polynomial rings. Consider the rings T and T ′ of real and complex trigonometric polynomials over the fields R and its algebraic extension C respectively ( see [6]). We construct the subrings T0 of T and T ′ 0, T ′ 1 of T ′. Then T0 is a BFD whereas T ′ 0 and T ′ 1 are Euclidean domains. We also discuss among these rings 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′′.
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