Constructing equivalence bimodules between noncommutative solenoids: A two-pronged approach

We revisit and generalize the application of a method introduced by Latrémolière Packer for constructing finitely generated projective modules over noncommutative solenoid C*-algebras. By realizing them as direct limits rotation algebras, constructs directed systems equivalence bimodules between algebras that satisfy necessary compatibility conditions to build Morita limit In irrational case, we use fixed projection in matrix algebra satisfying key condition an bimodule at each stage following construction Rieffel. From this, our main result shows two solenoids are equivalent if only such exists. also make additional observations about Heisenberg studied aforementioned authors connect constructions.