States on basic algebras
Mathematica Bohemica (2017)
- Volume: 142, Issue: 2, page 197-210
- ISSN: 0862-7959
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topChajda, Ivan, and Länger, Helmut. "States on basic algebras." Mathematica Bohemica 142.2 (2017): 197-210. <http://eudml.org/doc/288110>.
@article{Chajda2017,
abstract = {States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain pastings of Boolean algebras the construction of a state-morphism is shown.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Mathematica Bohemica},
keywords = {basic algebra; commutative basic algebra; symmetric basic algebra; state; homomorphism},
language = {eng},
number = {2},
pages = {197-210},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {States on basic algebras},
url = {http://eudml.org/doc/288110},
volume = {142},
year = {2017},
}
TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - States on basic algebras
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 2
SP - 197
EP - 210
AB - States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain pastings of Boolean algebras the construction of a state-morphism is shown.
LA - eng
KW - basic algebra; commutative basic algebra; symmetric basic algebra; state; homomorphism
UR - http://eudml.org/doc/288110
ER -
References
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- Chajda, I., Basic algebras and their applications. An overview, Proc. 81st Workshop on General Algebra (J. Czermak et al., eds.) Salzburg, Austria, 2011, Johannes Heyn, Klagenfurt (2012), 1-10. (2012) Zbl1280.06004MR2908429
- Chajda, I., Halaš, R., 10.1007/s00500-014-1365-y, Soft Comput. 19 (2015), 261-267. (2015) Zbl06654984DOI10.1007/s00500-014-1365-y
- Kalmbach, G., Orthomodular Lattices, London Mathematical Society Monographs 18. Academic Press, London (1983). (1983) Zbl0512.06011MR0716496
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