## Complemented modular lattices and regular rings |

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1-independent According to Proposition AL1 and ML antidistributive applying AL1 applying ML Applying Proposition arbitrary axis of perspective basis of rank Birkhoff called central element chain co(f complemented modular lattice complete complemented modular complete regular Consequently continuous geometry D-element decomposition denote dimension function direct sum equation exists an element find elements finitely generated module following properties follows at once follows from Proposition help of Proposition homogeneous basis idempotent implies independent inductive hypothesis lattice automorphism lattice isomorphism Lemma Maeda mapping ML and AL1 ML and Proposition ML we obtain morphism Neumann non-zero elements normal relative obvious partially ordered set principal left ideals projective geometry Proof Proposition 29 regular elements regular ring relation satisfies the conditions semi-homologous to zero shows Similarly simplex relative skewfield submodules Suppose Theorem Theorem 15 tion transfinite unit element validity