Vidinli algebras

In this paper, a new class of nonassociative algebras, Vidinli algebras, is defined based on recent work of Coşkun and Eden. These algebras are conic (or quadratic) algebras with the extra restriction that the commutator of any two elements is a scalar multiple of the unity. [Formula: see text]Over fields of characteristic not [Formula: see text], Vidinli algebras may be considered as generalizations of the Jordan algebras of Clifford type. However, in characteristic 2, the class of Vidinli algebras is much larger and includes the unitizations of anticommutative algebras.