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We develop elementary methods of computing the monoid for a directly-finite regular ring . We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.
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.
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