Molecules and linerly ordered ideals of MV-algebras.

Hoo, C. S.. "Molecules and linerly ordered ideals of MV-algebras.." Publicacions Matemàtiques 41.2 (1997): 455-465. <http://eudml.org/doc/41313>.

@article{Hoo1997,
abstract = {We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ \{0\} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime.},
author = {Hoo, C. S.},
journal = {Publicacions Matemàtiques},
keywords = {Algebras de Wajsberg; Lógica multivaluada; Algebras de Boole; Ideales; Grupo ordenado; Łukasiewicz calculus; many-valued logic; molecule; MV-algebra; minorants; Boolean elements; atoms; ideals},
language = {eng},
number = {2},
pages = {455-465},
title = {Molecules and linerly ordered ideals of MV-algebras.},
url = {http://eudml.org/doc/41313},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Hoo, C. S.
TI - Molecules and linerly ordered ideals of MV-algebras.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 455
EP - 465
AB - We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime.
LA - eng
KW - Algebras de Wajsberg; Lógica multivaluada; Algebras de Boole; Ideales; Grupo ordenado; Łukasiewicz calculus; many-valued logic; molecule; MV-algebra; minorants; Boolean elements; atoms; ideals
UR - http://eudml.org/doc/41313
ER -