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Equivalence of Idempotents
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A-F and H abelian idempotent abelian projections additivity of equivalence assume axiom F Baer ring satisfying central additivity central cover central idempotents central projection commuting ring continuous geometry decomposition direct sum direct summand division ring e)fe ef(l EP axiom equivalence relation satisfying equivalent projections gonal Hence Hilbert space hypothesis idempotent in eAe implies involution Jean-Pierre Serre jections left annihilator Let e,f Let f limit ordinal matrices matrix ring maximal modular lattice nilpotent nilpotent ideals non-zero central non-zero projection ordinary equivalence ortho orthogonal projections orthogonal sum parallelogram law partial isometries polar decomposition projections f prove g purely infinite ring real AW algebra regular ring relation satisfying axioms right annihilator right ideal right projection ring with involution RINGS OF OPERATORS satisfying axioms A-F satisfying the EP subring subset Suppose Theorem 22d Theorem 35 Theorem 54 theory tion two-sided ideal unit element write Zorn ring