Factorization Properties of Subrings in Trigonometric Polynomial Rings
نویسندگان
چکیده
We explore the subrings in trigonometric polynomial rings and their factorization properties. Consider the ring S′ of complex trigonometric polynomials over the field Q(i) (see [11]). We construct the subrings S′ 1, S′ 0 of S′ such that S′ 1 ⊆ S′ 0 ⊆ S′. Then S′ 1 is a Euclidean domain, whereas S′ 0 is a Noetherian HFD. We also characterize the irreducible elements of S′ 1, S′ 0 and discuss among these structures 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′′.
منابع مشابه
Subrings in Trigonometric Polynomial Rings
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...
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