Idempotents and Units of Matrix Rings over Polynomial Rings

Authors : Pramod KANWAR, Meenu KHATKAR, R K SHARMA

Pages : 147-169

Doi:10.24330/ieja.325941

View : 10 | Download : 11

Publication Date : 2017-07-11

Article Type : Research Paper

Abstract :The aim of this paper is to study idempotents and units in certain matrix rings over polynomial rings. More precisely, the conditions under which an element in $M_2insert ignore into journalissuearticles values(\mathbb{Z}_p[x]);$ for any prime $p$, an element in $M_2insert ignore into journalissuearticles values(\mathbb{Z}_{2p}[x]);$ for any odd prime $p$, and an element in $M_2insert ignore into journalissuearticles values(\mathbb{Z}_{3p}[x]);$ for any prime $p$ greater than 3 is an idempotent are obtained and these conditions are used to give the form of idempotents in these matrix rings. The form of elements in $M_2insert ignore into journalissuearticles values(\mathbb{Z}_2[x]);$ and elements in $M_2insert ignore into journalissuearticles values(\mathbb{Z}_3[x]);$ that are units is also given. It is observed that unit group of these rings behave differently from the unit groups of $M_2insert ignore into journalissuearticles values(\mathbb{Z}_2);$ and $M_2insert ignore into journalissuearticles values(\mathbb{Z}_3);$.  
Keywords : Idempotent, unit