Extensions of partially ordered partial abelian monoids

Sylvia Pulmannová

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 1, page 155-178
  • ISSN: 0011-4642

Abstract

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The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.

How to cite

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Pulmannová, Sylvia. "Extensions of partially ordered partial abelian monoids." Czechoslovak Mathematical Journal 56.1 (2006): 155-178. <http://eudml.org/doc/31022>.

@article{Pulmannová2006,
abstract = {The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.},
author = {Pulmannová, Sylvia},
journal = {Czechoslovak Mathematical Journal},
keywords = {abelian partially ordered groups; partially ordered partial abelian monoids; effect algebras; MV-algebras; Riesz decomposition properties; short exact sequences; extensions; abelian partially ordered groups; partially ordered partial abelian monoids; effect algebras},
language = {eng},
number = {1},
pages = {155-178},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extensions of partially ordered partial abelian monoids},
url = {http://eudml.org/doc/31022},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Pulmannová, Sylvia
TI - Extensions of partially ordered partial abelian monoids
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 155
EP - 178
AB - The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
LA - eng
KW - abelian partially ordered groups; partially ordered partial abelian monoids; effect algebras; MV-algebras; Riesz decomposition properties; short exact sequences; extensions; abelian partially ordered groups; partially ordered partial abelian monoids; effect algebras
UR - http://eudml.org/doc/31022
ER -

References

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