2016/06/15 by Amol Sasane, Sasane, Amol
Mathematics · #16S15 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Primary 46F05 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 13J99
paper · pdf · doi:10.48550/arxiv.1606.04685
openalex publication_date 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the ring of periodic distributions is a coherent ring (with the operations of pointwise addition and convolution) by showing that the isomorphic ring s' of the Fourier coefficients (of sequences of at most polynomial growth) with termwise operations is coherent. Moreover, it is shown that the subring ℓ^∞ of s' of all bounded sequences is coherent too, while the subring c of ℓ^∞ of all convergent sequences is not coherent. It is also observed that s' is a Hermite ring, but not a projective free ring.