University of Mohaghegh Ardabili Journal of Hyperstructures 2251-8436 6 1 2017 06 01 On the formal power series algebras generated by a vector space and a linear functional 1 9 2656 10.22098/jhs.2017.2656 EN A. R. Khoddami Department of Pure Mathematics, Shahrood University of Technology, P.O.Box 3619995161-316, Shahrood, Iran. Journal Article 2016 07 14 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]].  https://jhs.uma.ac.ir/article_2656_ae3ed705d53f88e8467701aa1f82a0be.pdf