Characterization of Differential and Pure Ideals in the Hurwitz Series Ring: Structural Insights and Formulations

This paper offers an in-depth investigation into pure ideals within the Hurwitz series ring. Specifically, by focusing on the Hurwitz series ring, denoted as HR over a ring R, we present a comprehensive characterization of differential ideals. In this paper, we prove that these differential ideals can be expressed in the form HI, where I represents an ideal in the underlying ring R. Through this analysis, a comprehensive understanding of the structure and properties of pure ideals within the Hurwitz series ring is achieved.

Abstract licence: CC BY

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