Self-small products of abelian groups

Josef Dvořák; Jan Žemlička

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 2, page 145-157
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Dvořák, Josef, and Žemlička, Jan. "Self-small products of abelian groups." Commentationes Mathematicae Universitatis Carolinae 62 63.2 (2022): 145-157. <http://eudml.org/doc/298512>.

@article{Dvořák2022,
abstract = {Let $A$ and $B$ be two abelian groups. The group $A$ is called $B$-small if the covariant functor $\{\rm Hom\}(A,-)$ commutes with all direct sums $B^\{(\kappa )\}$ 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.},
author = {Dvořák, Josef, Žemlička, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {self-small abelian group; slender group},
language = {eng},
number = {2},
pages = {145-157},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Self-small products of abelian groups},
url = {http://eudml.org/doc/298512},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Dvořák, Josef
AU - Žemlička, Jan
TI - Self-small products of abelian groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 2
SP - 145
EP - 157
AB - Let $A$ and $B$ be two abelian groups. The group $A$ is called $B$-small if the covariant functor ${\rm Hom}(A,-)$ commutes with all direct sums $B^{(\kappa )}$ 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.
LA - eng
KW - self-small abelian group; slender group
UR - http://eudml.org/doc/298512
ER -

References

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