Beschreibung:
<p>It was mentioned by Kaplansky that the parallelogram law is a key property for developing the dimension theory on the lattice of projections of a Baer <inline-formula content-type="math/mathml">
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</inline-formula>-ring, and he proved that this law follows from a pair of axioms: the EP and SR axioms. In this paper, it is shown that this law follows from only the SR axiom.</p>