Properties of Hurwitz polynomial and Hurwitz series rings

다국어 초록 (Multilingual 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.

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