Dimensional

This work introduces a new algebraic framework called Dimensional Algebraic Structures, in which elements are classified by a global, binary dimension invariant (0 or full). The dimension of an element is defined purely through the unital ambient algebra generated by its admissible global algebraic representatives, and is explicitly independent of any local differential behavior such as derivatives or Jacobians. The framework provides: A precise separation between global algebraic existence and local analytic properties. A dimensional analogue of classical algebraic notions such as zero divisors, integral domains, and fields. A notion of Dimensional Domain, where dimensional collapse under multiplication or addition is fully controlled. A notion of Dimensional Field, where invertibility and dimensional stability are required only for full-dimensional elements. The construction is intentionally abstract and representation-based, allowing the same dimensional logic to be instantiated over different ambient algebras. Local differential objects are excluded by design unless explicitly declared admissible, preventing ambiguity between constants, functions, and their local derivatives. This document is intended as a foundational preprint. It establishes definitions and structural axioms, leaving examples, morphisms, and further theory to subsequent work.