Holland’s theorem for pseudo-effect algebras

Anatolij Dvurečenskij

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 1, page 47-59
  • ISSN: 0011-4642

Abstract

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We give two variations of the Holland representation theorem for ℓ -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 M V -algebra can be represented as a pseudo-effect algebra or as a pseudo M V -algebra of automorphisms of some antilattice or of some linearly ordered set.

How to cite

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Dvurečenskij, 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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  1. 10.1017/S1446788700036806, J.  Austral. Math. Soc. 72 (2002), 427–445. (2002) MR1902211DOI10.1017/S1446788700036806
  2. Ideals of pseudo-effect algebras and their applications, Tatra Mt. Math. Publ. 27 (2003), 45–65. (2003) MR2026641
  3. New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. (2000) MR1861369
  4. Pseudoeffect algebras. I.  Basic properties, Inter. J.  Theor. Phys. 40 (2001), 685–701. (2001) MR1831592
  5. Pseudoeffect algebras. II.  Group representations, Inter. J.  Theor. Phys. 40 (2001), 703–726. (2001) MR1831593
  6. Pseudo- M V algebras, Multi. Val. Logic 6 (2001), 95–135. (2001) MR1817439
  7. 10.1090/S0002-9947-1972-0295991-3, Trans. Amer. Math. Soc. 166 (1972), 1–25. (1972) Zbl0235.06004MR0295991DOI10.1090/S0002-9947-1972-0295991-3
  8. 10.1007/s00500-002-0246-y, Soft Computing 8 (2003), 38–43. (2003) DOI10.1007/s00500-002-0246-y
  9. 10.1307/mmj/1028998976, Michigan Math.  J. 10 (1963), 399–408. (1963) Zbl0116.02102MR0158009DOI10.1307/mmj/1028998976

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