Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 251-256 (2007)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Ideal structure of Hurwitz series rings

Ali Benhissi

Department of Mathematics, Faculty of Sciences, 5000 Monastir, Tunisia, e-mail: ali${}_{_{-}}$

Abstract: 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 $\displaystyle c_n=\sum_{k=0}^n (_k^n)a_kb_{n-k}$ 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), 1845--1859. \item[L] Liu, Z.: Hermite and PS-rings of Hurwitz series. Comm. Algebra {\bf 28}(1) (2000), 299--305.

Full text of the article:

Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

© 2007 Heldermann Verlag
© 2007–2010 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition