Algorithm method for generalized derivations of two dimensional associative algebras

Abstract

The concept of generalized derivations of two dimensional associative algebras have been studied and their properties. The algorithm for finding generalized derivations have been given and its subspaces for the associative algebras [1]. The two dimensional associative algebras have 5 isomorphism classes of algebras. Each isomorphism classes have different table of multiplication. The algorithm; ∑_(t=1)^n▒〖(αγ_ij^t d_st-〖〖βd〗_ti γ〗_tj^s-〖〖γd〗_tj γ〗_it^s) 〗=0In case of i, j, s =1, 2, 3, … n is an easier way to find the result for generalized derivations. In complex associative algebras A, generalized derivations have seven subspaces which are 〖Der〗_((1,1,1)) A, 〖Der〗_((1,1,0)) A, 〖Der〗_((1,0,1)) A, 〖Der〗_((1,0,0)) A, 〖Der〗_((0,1,1)) A, 〖Der〗_((0,0,1)) A and 〖Der〗_((0,1,0)) A.