IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS

Authors : Jose Maria P BALMACEDA, Joanne Pauline P DATU

Pages : 1-12

Doi:10.24330/ieja.662942

View : 17 | Download : 11

Publication Date : 2020-01-07

Article Type : Research Paper

Abstract :We determine the forms of the nontrivial idempotents in the ring of $2\times 2$ matrices over the polynomial rings $\mathbb{Z}_{pq}[x]$ and $\mathbb{Z}_{p^2}[x]$, where $p$ and $q$ are any primes. Any such idempotent in the stated rings will be of a form in our list. Our work generalizes the results of Kanwar, Khatkar and Sharma insert ignore into journalissuearticles values(2017); who identified the forms of idempotents in $M_2insert ignore into journalissuearticles values(\mathbb{Z}_{2p}[x]);$ and $M_2insert ignore into journalissuearticles values(\mathbb{Z}_{3p}[x]);$.
Keywords : Idempotent, matrix ring, polynomial ring