Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 1, pp. 251256 (2007) 

Ideal structure of Hurwitz series ringsAli BenhissiDepartment of Mathematics, Faculty of Sciences, 5000 Monastir, Tunisia, email: ali${}_{_{}}$benhissi@yahoo.frAbstract: We study the ideals, in particular, the maximal spectrum and the set of idempotent elements, in rings of Hurwitz series. Let $A$ be a commutative ring with identity. The elements of the ring $HA$ of Hurwitz series over $A$ are formal expressions of the type $\displaystyle f=\sum_{i=0}^{\infty}a_iX^i$ where $a_i\in A$ for all $i$. Addition is defined termwise. The product of $f$ by $\displaystyle g=\sum_{i=0}^{\infty}b_iX^i$ is defined by $\displaystyle f*g=\sum_{n=0}^{\infty}c_nX^n$ where $\displaystyle c_n=\sum_{k=0}^n (_k^n)a_kb_{nk}$ and $(_k^n)$ is a binomial coefficient. Recently, many authors turned to this ring and discovered interesting applications in it. See for example [K] and [2]. The natural homomorphism $\epsilon:HA\longrightarrow A$, is defined by $\epsilon(f)=a_0$. \item[K] Keigher, W. F.: On the ring of Hurwitz series. Comm. Algebra {\bf 25}(6) (1997), 18451859. \item[L] Liu, Z.: Hermite and PSrings of Hurwitz series. Comm. Algebra {\bf 28}(1) (2000), 299305. Full text of the article:
Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.
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