A characterization of commutative basic algebras
Mathematica Bohemica (2009)
- Volume: 134, Issue: 2, page 113-120
- ISSN: 0862-7959
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topChajda, Ivan. "A characterization of commutative basic algebras." Mathematica Bohemica 134.2 (2009): 113-120. <http://eudml.org/doc/38079>.
@article{Chajda2009,
abstract = {A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.},
author = {Chajda, Ivan},
journal = {Mathematica Bohemica},
keywords = {lattice with section antitone involution; basic algebra; commutative basic algebra; MV-algebra; lattice with section antitone involution; basic algebra; MV-algebra},
language = {eng},
number = {2},
pages = {113-120},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A characterization of commutative basic algebras},
url = {http://eudml.org/doc/38079},
volume = {134},
year = {2009},
}
TY - JOUR
AU - Chajda, Ivan
TI - A characterization of commutative basic algebras
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 2
SP - 113
EP - 120
AB - A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
LA - eng
KW - lattice with section antitone involution; basic algebra; commutative basic algebra; MV-algebra; lattice with section antitone involution; basic algebra; MV-algebra
UR - http://eudml.org/doc/38079
ER -
References
top- Botur, M., Halaš, R., Finite commutative basic algebras are MV-algebras, (to appear) in Multiple-Valued Logic and Soft Computing.
- 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., 10.7151/dmgaa.1073, Discuss. Math., Gener. Algebra Appl. 24 (2004), 31-42. (2004) Zbl1082.03055MR2117673DOI10.7151/dmgaa.1073
- Chajda, I., Halaš, R., 10.1007/s10773-007-9468-1, Int. J. Theor. Phys. 47 (2008), 261-267. (2008) Zbl1145.06003MR2377053DOI10.1007/s10773-007-9468-1
- Chajda, I., Halaš, R., Kühr, J., Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19-33. (2005) Zbl1099.06006MR2160352
- Cignoli, R. L. O., D'Ottaviano, M. L., Mundici, D., Algebraic Foundations of Many-Valued Reasoning, Kluwer Acad. Publ., Dordrecht (2000). (2000) Zbl0937.06009MR1786097
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