Abstract
Using the facts that the disk algebra and the Wiener algebra are not coherent, we prove that the polydisc algebra, the ball algebra, and the Wiener algebra of the polydisc are not coherent.
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References
Amar E.: Non cohérence de certains anneaux de fonctions holomorphes. Illinois Journal of Mathematics 25, 68–73 (1981)
Glaz S.: Commutative coherent rings: historical perspective and current developments. Nieuw Archief voor Wiskunde 10(4), 37–56 (1992)
Hickel M.: Non cohérence de certains anneaux de fonctions holomorphes. Illinois Journal of Mathematics 34, 515–525 (1990)
Kaplansky I.: Commutative Rings. Allyn and Bacon, Boston, Mass (1970)
McVoy W.S., Rubel L.A.: Coherence of some rings of functions. Journal of Functional Analysis 21, 76–87 (1976)
Mortini R., von Renteln M.: Ideals in the Wiener algebra W +. Journal of the Australian Mathematical Society Series A 46, 220–228 (1989)
A. Quadrat, The fractional representation approach to synthesis problems: an algebraic analysis viewpoint. I. (Weakly) doubly coprime factorizations, SIAM Journal on Control Optimization 42 (2003), 266–299.
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Mortini, R., Sasane, A. Noncoherence of some rings of holomorphic functions in several variables as an easy consequence of the one-variable case. Arch. Math. 101, 525–529 (2013). https://doi.org/10.1007/s00013-013-0592-2
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DOI: https://doi.org/10.1007/s00013-013-0592-2