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. |
Other formats:
BibTeX
LaTeX
RIS
@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.
|