# Molecules and linerly ordered ideals of MV-algebras.

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 455-465
- ISSN: 0214-1493

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topHoo, 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 -

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