| PASEKA, Jan and Zdenka RIEČANOVÁ. Isomorphism theorems on generalized effect algebras based on atoms. INFORMATION SCIENCES. NEW YORK, NY 10010-1710 USA: ELSEVIER SCIENCE INC, 2009, vol. 179, No 5, p. 521-528. ISSN 0020-0255. |
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@article{837831,
author = {Paseka, Jan and Riečanová, Zdenka and Riečanová, Zdenka},
article_location = {NEW YORK, NY 10010-1710 USA},
article_number = {5},
keywords = {Non-classical logics; D-posets; Effect algebras; MV-algebras; States; Probabilities on quantum structures},
language = {eng},
issn = {0020-0255},
journal = {INFORMATION SCIENCES},
note = {doi: 10.1016/j.ins.2008.08.016},
title = {Isomorphism theorems on generalized effect algebras based on atoms},
volume = {179},
year = {2009}
}
TY - JOUR
ID - 837831
AU - Paseka, Jan - Riečanová, Zdenka - Riečanová, Zdenka
PY - 2009
TI - Isomorphism theorems on generalized effect algebras based on atoms
JF - INFORMATION SCIENCES
VL - 179
IS - 5
SP - 521-528
EP - 521-528
PB - ELSEVIER SCIENCE INC
SN - 00200255
N1 - doi: 10.1016/j.ins.2008.08.016
KW - Non-classical logics
KW - D-posets
KW - Effect algebras
KW - MV-algebras
KW - States
KW - Probabilities on quantum structures
N2 - A well-known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub-generalized effect algebra and simultaneously a proper order ideal, the set-theoretic complement of which is its dual poset. We show that two non-isomorphic generalized effect algebras (even finite ones) may have isomorphic effect algebraic extensions. For Archimedean atomic lattice effect algebras we prove "Isomorphism theorem based on atoms". As an application we obtain necessary and sufficient conditions for isomorphism of two prelattice Archimedean atomic generalized effect algebras with common (or isomorphic) effect algebraic extensions.
ER -
PASEKA, Jan and Zdenka RIEČANOVÁ. Isomorphism theorems on generalized effect algebras based on atoms. \textit{INFORMATION SCIENCES}. NEW YORK, NY 10010-1710 USA: ELSEVIER SCIENCE INC, 2009, vol.~179, No~5, p.~521-528. ISSN~0020-0255.
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