The Matrix Ring Homomorphisms are Applicable to Skewed Generalized Composite Series Rings

Let (ܴ1[[ܵ1, ≤1, ߱1]]) and ܯ݊)ܴ2]]ܵ2,≥ 2, ߱2 ([[be a matrix rings over skew generalized power series rings, where ܴ1, ܴ2 are commutative rings with an identity element, (ܵ1, ≤1), (ܵ2, ≤2) are strictly ordered monoids, ߱1: ܵ1 → ܧ݊݀)ܴ1(, ߱2: ܵ2 → ܧ݊݀)ܴ2 (are monoid homomorphisms. In this research, we define a mapping ݎ from (ܴ1[[ܵ1, ≤1, ߱1]]) to ܯ݊)ܴ2]]ܵ2,≥ 2, ߱2 ([[by using a strictly ordered monoid homomorphism ߜ:) ܵ1,≥ 1) → (ܵ2,≥ 2(, and ring homomorphisms ߤ: ܴ1 → ܴ2 and ߪ: ܴ1]]ܵ1,≥ 1, ߱1 → [[ܴ2]]ܵ2,≥ 2, ߱2[[. Furthermore, we prove that ݎ is a ring homomorphism, and also we give the sufficient conditions for ݎ to be a monomorphism, epimorphism, and isomorphism.