“After completely reducible systems, the notions of solvable and nilpotent systems are discussed, where general identities are considered instead of the usual commutativity.”
“It is subjected to certain conditions and, for example, to the rules of commutativity and associativity of addition.”
“While commutativity holds for many systems, such as the real or complex numbers, there are other systems, such as the system of n × n matrices or the system of quaternions, in which commutativity of multiplication is invalid.”