A Schröder-Bernstein theorem in Baer*-rings with lattice-theoretic proof

Hakeda, Jôsuke

doi:10.1090/S0002-9939-1979-0534403-0

A Schröder-Bernstein theorem in Baer$^{\ast }$-rings with lattice-theoretic proof
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Proc. Amer. Math. Soc. 76 (1979), 131-132 Request permission

Abstract:

The Schröder-Bernstein theorem (SB-theorem) for $*$-equivalence of projections of a $\mathrm {Baer}^*$-ring is known. Here, we will prove an SB-theorem for algebraic equivalence (Theorem A) as a consequence of a lattice-theoretic SB-theorem (Theorem B). Theorem A and the known result about $*$-equivalence will be derived from Theorem B.

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