IDEMPOTENT MATRIX OVER SKEW GENERALIZED POWER SERIES RINGS - Ahmad Faisol; Fitriani Fitriani (Diponegoro University, 2022)
Let R[[S,≤,ω]] be a skew generalized power series ring, with R is a ring with an identity element, (S,≤) a strictly ordered monoid, and ω:S→ End(R) a monoid homomorphism. We define the set of all matrices over R[[S,≤,ω]], denoted by M_n(R[[S,≤,ω]]). With the addition and multiplication matrix operations, M_n(R[[S,≤,ω]]) becomes a ring. In this paper, we determine the sufficient conditions for R, (S,≤), and ω, so the element of M_n(R[[S,≤,ω]]) is an idempotent matrix.