Structural and Classification Theorems for Weyl-Type Algebras over Expolynomial Rings

This paper introduces and systematically studies Weyl-type, Witt-type, and non-associative algebras defined over expolynomial rings – commutative rings generated by exponential functions $e^{\alpha x}$, exponentials of exponentials $e^{\pm x^p{e}^t}$, and power functions $x^{\alpha }$ for $\alpha$ in an additive subgroup $\text{cA}$ of a characteristic zero field $\text{FF}$. We establish several fundamental structural results: scalar extensions preserve both the algebraic structure and simplicity; intermediate subalgebras associated with subgroups $\text{ZZ}\subseteq \text{cB}\subseteq \text{cA}$ remain simple; the algebra of graded derivations is isomorphic to a semidirect product $\text{Weyl}{e}^{\pm x^p{e}^t},e^{\text{cA}x},x^{\text{cA}}⋊{\text{FF}}^n$; tensor products over disjoint variable sets decompose naturally into larger algebras; and a complete isomorphism criterion is given, showing that isomorphism depends precisely on the orbit of the parameter $p$ under the automorphism group of $\text{cA}$ and the equality of the deformation parameter $t$. These theorems generalize classical results on Weyl and Witt algebras, provide new families of simple algebras, and offer a foundation for further research in deformation theory, representation theory, and cohomology.