On the formal power series algebras generated by a vector space and a linear functional

Let R be a vector space ( on C) and ϕ be an element of R∗ (the dual space of R), the product r · s = ϕ(r)s converts R into an associative algebra that we denote it by Rϕ. We characterize the nilpotent, idempotent and the left and right zero divisor elements of Rϕ[[x]]. Also we show that the set of a...

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Bibliographic Details
Main Author: A. R. Khoddami
Format: Article
Language:English
Published: University of Mohaghegh Ardabili 2017-06-01
Series:Journal of Hyperstructures
Subjects:
Online Access:https://jhs.uma.ac.ir/article_2656_ae3ed705d53f88e8467701aa1f82a0be.pdf
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Summary:Let R be a vector space ( on C) and ϕ be an element of R∗ (the dual space of R), the product r · s = ϕ(r)s converts R into an associative algebra that we denote it by Rϕ. We characterize the nilpotent, idempotent and the left and right zero divisor elements of Rϕ[[x]]. Also we show that the set of all nilpotent elements and also the set of all left zero divisor elements of Rϕ[[x]] are ideals of Rϕ[[x]].
ISSN:2251-8436
2322-1666