TY - JOUR
T1 - Lattice-ordered effect algebras and L-algebras
AU - Wu, Yali
AU - Wang, Jing
AU - Yang, Yichuan
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/8/15
Y1 - 2019/8/15
N2 - It is known that many logical algebras can be considered as L-algebras. In this paper, we first construct an effect algebra (E,⊕,0,1) that cannot be converted into an L-algebra (E,→,0,1) with negation such that x→0 is the orthosupplement. Then we prove that every lattice-ordered effect algebra gives rise to an L-algebra with the same orthosupplement. Finally, we characterize LE-L-algebras as lattice-ordered effect algebras. As an application, we extend those results obtained in some recent references for orthomodular lattices and MV-algebras.
AB - It is known that many logical algebras can be considered as L-algebras. In this paper, we first construct an effect algebra (E,⊕,0,1) that cannot be converted into an L-algebra (E,→,0,1) with negation such that x→0 is the orthosupplement. Then we prove that every lattice-ordered effect algebra gives rise to an L-algebra with the same orthosupplement. Finally, we characterize LE-L-algebras as lattice-ordered effect algebras. As an application, we extend those results obtained in some recent references for orthomodular lattices and MV-algebras.
KW - Effect algebras
KW - L-algebras
KW - MV-algebras
KW - Orthomodular lattices
UR - https://www.scopus.com/pages/publications/85052829566
U2 - 10.1016/j.fss.2018.08.013
DO - 10.1016/j.fss.2018.08.013
M3 - 文章
AN - SCOPUS:85052829566
SN - 0165-0114
VL - 369
SP - 103
EP - 113
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -