Abstract
The idempotents, resp. Hermitian idempotents, of a unital ring, resp. involutive unital ring, form an orthomodular poset. We study these Orthomodular posets for rings of matrices over the integers modulom or over Galois fields. In analogy to the Hilbert space situation we look for idempotent matrices (projections) corresponding to splitting subspaces of finite-dimensional vector spaces.
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