Author/Authors :
Kanwar, Pramod Department of Mathematics - Ohio University-Zanesville, USA , Khatkar, Meenu Department of Mathematics - Indian Institute of Technology, India , Sharma, R. K. Department of Mathematics - Indian Institute of Technology, India
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 M2(Zp[x]) for any prime p, an element in M2(Z2p[x]) for any
odd prime p, and an element in M2(Z3p[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 M2(Z2[x]) and
elements in M2(Z3[x]) that are units is also given. It is observed that unit
group of these rings behave differently from the unit groups of M2(Z2) and
M2(Z3).
