Linear relations defined on modules of finite length are shift equivalent to bijective mappings.
Mrozek, Leray functor and cohomological Conley index for discrete dynam- ical systems, Transactions of the American Mathematical Society , 318 (1990), 1, 149–178
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Linear Relations of Finite Length Modules are Shift Equivalent to Maps
Linear relations defined on modules of finite length are shift equivalent to bijective mappings.