**Background:**First examples of simple nonassociative superalgebras were constructed by Shestakov in (1991 and 1992). Since then many researchers showed interest towards the study of superalgebras and superalgebras of vector type.

**Multiplication in M is uniquely defined by a fixed finite set of derivations and by elements of A. The types of derivations used in this article to obtain the results are the near derivation δ**

**Materials and Methods:**_{x,y}: a ↦ (a, x, y) the derivation D : a ↦ (x, a, x) and the derivation D

_{ij}: a ↦ (x

_{i},a, x

_{j})

**Results:**The flexible Lie-admissible superalgebra F

_{FLSA}[φ; x] over a 2, 3-torsion free field Φ on one odd generator e is isomorphic to the twisted superalgebra B

_{0}(Φ[Γ], D, γ

_{0}) with the free generator . In a 2, 3-torsion free flexible Lie-admissible superalgebras of vector type F, the even part A is differentiably simple, associative and commutative algebra and the odd part M is a finitely generated associative and commutative A-bimodule.

**Conclusion:**A connection between the integral domains, the finitely generated projective modules over them, the derivations of an integral domain and the flexible Lie-admissible superalgebras of vector type has been established. If A is an integral domain and M = Ax

_{1}+…+Ax

_{n}be a finitely generated projective A-module of rank 1, then F (A, Δ, Γ) is a flexible Lie-admissible superalgebra with even part A and odd part M provided that the mapping M = Ax

_{i}+…+Ax

_{n}is a nonzero derivation of A into the A-module (M⊗

_{A}M)*, Δ = {D

_{ij}|i, j = 1,…, n} is a set of derivations of A where D

_{ij}(a) = ā (x⊗x

_{j}).]]>