By an L-algebra we mean a power-associative nonassociative algebra (not necessarily finite-dimensional) over a field F in which every subalgebra generated by a single element is a left ideal. An H-algebra is a power-associative algebra in which every subalgebra is an ideal. The H-algebras were characterized by D. L. Outcalt in [2]. Let Sα be the semigroup with cardinality α such that if x, y ∊ Sα then xy = y. Consider the algebra over a field F with basis Sα. Such an algebra is an L-algebra that is not an H-algebra unless Sα contains only one element. In this paper we will prove that an algebra A over a field F with char. ≠ 2 is an L-algebra if and only if it is either an H-algebra or has a basis Sα where α is the dimension of A.