Conjugated algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2009)
- Volume: 48, Issue: 1, page 17-23
- ISSN: 0231-9721
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topChajda, Ivan. "Conjugated algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 48.1 (2009): 17-23. <http://eudml.org/doc/35180>.
@article{Chajda2009,
abstract = {We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone involutions on the corresponding intervals.},
author = {Chajda, Ivan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Conjugated algebras; basic algebra; section antitone involution; quasiorder; conjugated algebras; basic algebras; section antitone involution; quasiorder},
language = {eng},
number = {1},
pages = {17-23},
publisher = {Palacký University Olomouc},
title = {Conjugated algebras},
url = {http://eudml.org/doc/35180},
volume = {48},
year = {2009},
}
TY - JOUR
AU - Chajda, Ivan
TI - Conjugated algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2009
PB - Palacký University Olomouc
VL - 48
IS - 1
SP - 17
EP - 23
AB - We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone involutions on the corresponding intervals.
LA - eng
KW - Conjugated algebras; basic algebra; section antitone involution; quasiorder; conjugated algebras; basic algebras; section antitone involution; quasiorder
UR - http://eudml.org/doc/35180
ER -
References
top- Chajda, I., Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carol. 44 (2003), 577–585. (2003) Zbl1101.06003MR2062874
- Chajda, I., Emanovský, P., Bounded lattices with antitone involutions and properties of MV-algebras, Discuss. Math., Gener. Algebra and Appl. 24 (2004), 31–42. (2004) Zbl1082.03055MR2117673
- Chajda, I., Halaš, R., Kühr, J., Semilattice Structures, Heldermann Verlag, Lemgo, 2007. (2007) Zbl1117.06001MR2326262
- Chajda, I., Kühr, J., A non-associative generalization of MV-algebras, Math. Slovaca 57 (2007), 1–12. (2007) Zbl1150.06012MR2357826
- Cignoli, R. L. O., D’Ottaviano, M. L., Mundici, D., Algebraic Foundations of Many-valued Reasoning, Kluwer Acad. Publ., Dordrecht, 2000. (2000) MR1786097
- Halaš, R., Plojhar, L., Weak MV-algebras, Math. Slovaca 58 (2008), 1–10. (2008) Zbl1174.06009MR2399238
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