Factorization properties of subrings in trigonometric polynomial rings
Keyword(s):
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''. .
1991 ◽
Vol 109
(2)
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pp. 287-297
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1978 ◽
Vol 1
(4)
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pp. 433-438
2020 ◽
pp. 2150113
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1968 ◽
Vol 64
(3)
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pp. 721-730
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1980 ◽
Vol 3
(2)
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pp. 237-245
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1993 ◽
Vol 55
(2)
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pp. 238-245