IDEMPOTENT ELEMENTS IN MATRIX RING OF ORDER 2 OVER POLYNOMIAL RING Z_p^2q[x] - Arifin, Muchammad Choerul; Ernanto, Iwan (Diponegoro University, 2023)
An idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements, 0 and 1, these particular idempotent elements are commonly referred to as the trivial idempotent elements However, in the case of rings Z_n and Z_n[x] it is possible to have non-trivial idempotent elements. In this paper, we will investigate the idempotent elements in the polynomial ring Z_p^2q[x] with p,q different primes. Furthermore, the form and characteristics of non-trivial idempotent elements in M_2(Z_p^2q[x]) will be investigated. The results showed that there are 4 idempotent elements in Z_p^2q[x] and 7 idempotent elements in M_2(Z_p^2q[x]).