Directoid groups

Barry J. Gardner; Michael M. Parmenter

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 3, page 669-681
  • ISSN: 0011-4642

Abstract

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We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.

How to cite

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Gardner, Barry J., and Parmenter, Michael M.. "Directoid groups." Czechoslovak Mathematical Journal 58.3 (2008): 669-681. <http://eudml.org/doc/37859>.

@article{Gardner2008,
abstract = {We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.},
author = {Gardner, Barry J., Parmenter, Michael M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {directed abelian group; variety; directed abelian group; variety},
language = {eng},
number = {3},
pages = {669-681},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Directoid groups},
url = {http://eudml.org/doc/37859},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Gardner, Barry J.
AU - Parmenter, Michael M.
TI - Directoid groups
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 669
EP - 681
AB - We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
LA - eng
KW - directed abelian group; variety; directed abelian group; variety
UR - http://eudml.org/doc/37859
ER -

References

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