Primitive idempotents in a semisimple ring

Abstract

Let [Formula: see text] be distinct primes, [Formula: see text] odd. Let [Formula: see text], where [Formula: see text] be an integer. In this paper, it is observed that the explicit expressions of primitive idempotents from [Formula: see text] are sufficient to compute the explicit expressions of primitive idempotent in semisimple ring [Formula: see text]. It is also shown that the results obtained in [A. Sahni and P. T. Sehgal, Minimal cyclic codes of length [Formula: see text], Finite Fields Appl. 18(5) (2012) 1017–1036; P. Kumar and S. K. Arora, [Formula: see text]-mapping and primitive idempotents in semisimple ring [Formula: see text], Comm. Algebra 41(10) (2013) 3679–3694] are simple corollaries to the results obtained in the paper.