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Keywords:
small module; self-injectivity; von Neumann regular ring; purely infinite rings; direct sums; direct products; strongly inaccessible cardinals
small module; self-injectivity; von Neumann regular ring; purely infinite rings; direct sums; direct products; strongly inaccessible cardinals
Summary:
Module is said to be small if it is not
a union of strictly increasing infinite
countable chain of submodules. We show
that the class of all small modules
over self-injective purely infinite
ring is closed under direct products
whenever there exists no strongly
inaccessible cardinal.
References:
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