On S-Evolution Algebras and Their Enveloping Algebras

In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of S-evolution algebras, and prove such derivations can be extended to their enveloping algebras under certain conditions.