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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
University of Mohaghegh Ardabili
2017-06-01
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| 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]]. |
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| ISSN: | 2251-8436 2322-1666 |