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On the formal power series algebras generated by a vector space and a linear functional | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 1، شهریور 2017، صفحه 1-9 اصل مقاله (266.75 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2656 | ||
| نویسنده | ||
| A. R. Khoddami* | ||
| Department of Pure Mathematics, Shahrood University of Technology, P.O.Box 3619995161-316, Shahrood, Iran. | ||
| چکیده | ||
| 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]]. | ||
| کلیدواژه‌ها | ||
| Vector space؛ Formal power series algebra؛ Nilpotent؛ Idempotent؛ Algebraic homomorphism | ||
| مراجع | ||
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[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. | ||
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آمار تعداد مشاهده مقاله: 45 تعداد دریافت فایل اصل مقاله: 54 |
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