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An Algebraic Framework for Boolean Vector Spaces Over Almost Distributive Lattices

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  • Ramesh Sirisetti
  • Ravikumar Bandaru
  • Rahul Shukla

Abstract

This paper establishes a systematic study of Boolean vector spaces over relatively complemented almost distributive lattices. Motivated by the classical theory of Boolean vector spaces, we generalize these notions to a broader algebraic framework in which lattice operations replace traditional scalar multiplication. The work unifies and extends earlier approaches to distributive lattice theory, Boolean algebras, and vector lattice theory. We construct Boolean subspaces and establish projection operators.

Suggested Citation

  • Ramesh Sirisetti & Ravikumar Bandaru & Rahul Shukla, 2026. "An Algebraic Framework for Boolean Vector Spaces Over Almost Distributive Lattices," Journal of Mathematics, Hindawi, vol. 2026, pages 1-6, July.
    • Handle: RePEc:hin:jjmath:9450447
    DOI: 10.1155/jom/9450447
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