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Algebra |
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Authors: Lamarr Widmer
If * is a binary operation on a set S, an element a is an idempotent for * if a*a=a . In this paper, we provide an alternative equivalent definition for idempotents in a ring with unity. This definition facilitates the calculations in several theorems characterizing the idempotents in rings of the form Z_n . This material was developed by the author while teaching a one semester undergraduate class in modern algebra. Some of this material was presented to students in that class and we believe all of it is suitable for students after a basic introduction to rings. We include numerous theorems determining the number of idempotents in Z_n for various factorizations of n . These theorems, along with specific examples and calculations, lead to the eventual general theorem which shows how the number of idempotents in Z_n is determined by the number of prime divisors of n.
Comments: 14 Pages. (Note by viXra Admin: Please cite and list scientific references)
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[v1] 2026-02-09 21:28:11
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