Journal of Frame and Matrix Theory

Journal of Frame and Matrix Theory

A study of expansive automorphisms in a pointfree topology

Document Type : Original Article

Authors
Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran
10.22034/jfmt.2026.519010.1029
Abstract
We introduce and investigate expansive automorphisms in the setting of frames and commutative rings, providing a point-free extension of classical expansivity in topological dynamics. We define the notion of uniform refinement expansive automorphisms for frames and rings and establish their fundamental properties and characterizations in terms of covers, refinements, z-ideals, and radical ideals. A dual correspondence between expansive frame isomorphisms and expansive homeomorphisms on their spectra is developed via functorial constructions, yielding a bridge between algebraic and topological dynamics. Furthermore, we prove finiteness results for positively expansive systems, showing that frames admitting such automorphisms have finite maximal spectra, with applications to compact spaces. For function rings R(L) and C(X), we establish equivalences between algebraic expansivity and classical topological expansivity.
Keywords
Subjects


Articles in Press, Accepted Manuscript
Available Online from 12 November 2026

  • Receive Date 24 April 2025
  • Revise Date 17 February 2026
  • Accept Date 20 August 2026