λ-Mapping and Primitive Idempotents in Semisimple Ring ℜ m

Abstract

Let , where r ≥ 2, {p i |1 ≤ i ≤ r} is a set of distinct primes such that , for i ≠ j, 1 ≤ i, j ≤ r and α i ≥ 1. Let GF(l) be a finite field of prime order l, where l is a primitive root modulo for each i, 1 ≤ i ≤ r and is co-prime to m. A simple method (named as λ-method) for obtaining cyclotomic cosets modulo m and the explicit expressions of primitive idempotents in semisimple ring is discussed.