Directoids with sectionally switching involutions
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)
- Volume: 45, Issue: 1, page 35-41
- ISSN: 0231-9721
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topChajda, Ivan. "Directoids with sectionally switching involutions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 35-41. <http://eudml.org/doc/32507>.
@article{Chajda2006,
abstract = {It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities.},
author = {Chajda, Ivan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Directoid; commutative directoid; semilattice; involution; implication algebra; sectionally switching mapping; directoid; commutative directoid; semilattice; involution; implication algebra; sectionally switching mapping},
language = {eng},
number = {1},
pages = {35-41},
publisher = {Palacký University Olomouc},
title = {Directoids with sectionally switching involutions},
url = {http://eudml.org/doc/32507},
volume = {45},
year = {2006},
}
TY - JOUR
AU - Chajda, Ivan
TI - Directoids with sectionally switching involutions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 35
EP - 41
AB - It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities.
LA - eng
KW - Directoid; commutative directoid; semilattice; involution; implication algebra; sectionally switching mapping; directoid; commutative directoid; semilattice; involution; implication algebra; sectionally switching mapping
UR - http://eudml.org/doc/32507
ER -
References
top- Abbott J. C., Semi-boolean algebras, Matem. Vestnik 4 (1967), 177–198. (1967) MR0239957
- Chajda I., Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carol. 44 (2003), 577–585. Zbl1101.06003MR2062874
- Chajda I., Halaš R., Kühr J., Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged), 71 (2005), 19–33. Zbl1099.06006MR2160352
- Ježek J., Quackenbush R., Directoids: algebraic models of up-directed sets, , Algebra Universalis 27 (1990), 49–69. (1990) MR1025835
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