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

Document Type : Research Paper

Author

Department of Pure Mathematics, Shahrood University of Technology, P.O.Box 3619995161-316, Shahrood, Iran.

Abstract

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]]. 

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References

[1] A. R. Khoddami and H. R. E. Vishki, The higher duals of a Banach algebra induced by a bounded linear functional, Bull. Math. Anal. Appl., 3 (2011), 118–122.
[2] A. R. Khoddami, Strongly zero-product preserving maps on normed algebras in-duced by a bounded linear functional, Khayyam J. Math., 1 (2015), no. 1, 107–114.
[3] A. R. Khoddami and M. Hasani, Endomorphisms and automorphisms of certain semigroups, J. Semigroup Theory Appl., available online at http://scik.org.
[4] A. R. Khoddami, The second dual of strongly zero product preserving maps, to appear.
Journal of Hyperstructures
Volume 6, Issue 1
June 2017
Pages 1-9

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