Abstract
IN model theory, Zil’ ber has proved that any model of nontrivial -categorical theory is verysimilar to a module or field. So some people wanted to prove the famous Vaught’s conjec-ture for superstable theories of modules. Later, Buechler proved that the Vaught’s conjectureis true for the theories of modules with Morley rank 1. In order to reduce Vaught’s conjec-ture for superstablc theories of modules, Prest suggested discussing the preservation of stabili-ty--theory properties of modules when the underlying ring of the modules changes. Zieglergave some preservation theorems of clementary properties of the theory of modules in ref.
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