Holland’s theorem for pseudo-effect algebras
Czechoslovak Mathematical Journal (2006)
- Volume: 56, Issue: 1, page 47-59
- ISSN: 0011-4642
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topDvurečenskij, Anatolij. "Holland’s theorem for pseudo-effect algebras." Czechoslovak Mathematical Journal 56.1 (2006): 47-59. <http://eudml.org/doc/31016>.
@article{Dvurečenskij2006,
abstract = {We give two variations of the Holland representation theorem for $\ell $-groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo $MV$-algebra can be represented as a pseudo-effect algebra or as a pseudo $MV$-algebra of automorphisms of some antilattice or of some linearly ordered set.},
author = {Dvurečenskij, Anatolij},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudo-effect algebra; pseudo $MV$-algebra; antilattice; prime ideal; automorphism; unital po-group; unital $\ell $-group; pseudo-effect algebra; pseudo-MV-algebra; antilattice; prime ideal; automorphism; unital po-group; unital -group},
language = {eng},
number = {1},
pages = {47-59},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Holland’s theorem for pseudo-effect algebras},
url = {http://eudml.org/doc/31016},
volume = {56},
year = {2006},
}
TY - JOUR
AU - Dvurečenskij, Anatolij
TI - Holland’s theorem for pseudo-effect algebras
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 47
EP - 59
AB - We give two variations of the Holland representation theorem for $\ell $-groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo $MV$-algebra can be represented as a pseudo-effect algebra or as a pseudo $MV$-algebra of automorphisms of some antilattice or of some linearly ordered set.
LA - eng
KW - pseudo-effect algebra; pseudo $MV$-algebra; antilattice; prime ideal; automorphism; unital po-group; unital $\ell $-group; pseudo-effect algebra; pseudo-MV-algebra; antilattice; prime ideal; automorphism; unital po-group; unital -group
UR - http://eudml.org/doc/31016
ER -
References
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