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Cyclotomic Cosets of Primitive Idempotents in Semi Simple Ring

Ranjeet Singh

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Source: Crossref

Published: Sep 17, 2026

DOI: 10.14445/22315373/ijmtt-v72i8p102

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Source abstract

We consider the ring 𝑅16π‘π‘›π‘žπ‘š = 𝐺𝐹(𝑙)[π‘₯]/(π‘₯16π‘π‘›π‘žπ‘š βˆ’ 1)where 𝑝,π‘ž,𝑙 are distinct odd primes, l is a primitive root, both modulo 𝑝𝑛 and π‘žπ‘š such that 𝑔𝑐𝑑(πœ‘(𝑝𝑛),πœ‘(π‘žπ‘š))= 𝑑 .Explicit expressions for all the 16(π‘š Γ— 𝑛 Γ— 𝑑 + π‘š + 𝑛 +1) Cyclotomic Coset are obtained, 𝑝 does not divide qβˆ’1 and 𝑙 is of the form 16k+1.

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Cyclotomic Cosets of Primitive Idempotents in Semi Simple Ring β€” Mathematical Frontier Network