C4*-modules are stable under exact sequences when summand-lifting and factor-control hold, with ambient realizations in semisimple modules over any ring.
Nielsen,Square-free modules with the exchange property, Journal of Algebra323(2010), no
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Exact-Sequence Stability and Ambient Realizations for $C4^{\ast}$-Modules
C4*-modules are stable under exact sequences when summand-lifting and factor-control hold, with ambient realizations in semisimple modules over any ring.