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Self-small products of abelian groups

Josef Dvořák, Jan Žemlička (2022)

Commentationes Mathematicae Universitatis Carolinae

Let A and B be two abelian groups. The group A is called B -small if the covariant functor Hom ( A , - ) commutes with all direct sums B ( κ ) and A is self-small provided it is A -small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.

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