Properties of Hurwitz polynomial and Hurwitz series rings
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 837-849
Published online May 31, 2018
Jesse Elliott, Hwankoo Kim
California State University at Channel Islands, Hoseo University
Abstract : In this paper, we study the closedness such as seminomality and $t$-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.
Keywords : Hurwitz series ring, $t$-closed, seminormal, weakly normal, piecewise Noetherian ring, Noetherian spectrum
MSC numbers : Primary 13F20, 13F25; Secondary 13A15, 13B21, 13E99
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