Geodesic
States on basic algebras
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 197-210.

Voir la notice de l'article dans Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2016.0056-14
Classification : 03G25, 06C15, 06D35
Mots-clés : basic algebra; commutative basic algebra; symmetric basic algebra; state; homomorphism 
@article{10_21136_MB_2016_0056_14,
     author = {Chajda, Ivan and L\"anger, Helmut},
     title = {States on basic algebras},
     journal = {Mathematica Bohemica},
     pages = {197--210},
     publisher = {mathdoc},
     volume = {142},
     number = {2},
     year = {2017},
     doi = {10.21136/MB.2016.0056-14},
     mrnumber = {3660176},
     zbl = {06738580},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0056-14/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Länger, Helmut
TI  - States on basic algebras
JO  - Mathematica Bohemica
PY  - 2017
SP  - 197
EP  - 210
VL  - 142
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0056-14/
DO  - 10.21136/MB.2016.0056-14
LA  - en
ID  - 10_21136_MB_2016_0056_14
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Länger, Helmut
%T States on basic algebras
%J Mathematica Bohemica
%D 2017
%P 197-210
%V 142
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0056-14/
%R 10.21136/MB.2016.0056-14
%G en
%F 10_21136_MB_2016_0056_14
Chajda, Ivan; Länger, Helmut. States on basic algebras. Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 197-210. doi : 10.21136/MB.2016.0056-14. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0056-14/

Cité par Sources :