Molecules and linerly ordered ideals of MV-algebras.
Hoo, C. S.
Publicacions Matemàtiques, Tome 41 (1997), p. 455-465 / Harvested from Biblioteca Digital de Matemáticas
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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.

Publié le : 1997-01-01
DMLE-ID : 3846 
@article{urn:eudml:doc:41313,
     title = {Molecules and linerly ordered ideals of MV-algebras.},
     journal = {Publicacions Matem\`atiques},
     volume = {41},
     year = {1997},
     pages = {455-465},
     mrnumber = {MR1485495},
     zbl = {0897.06015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41313}
}

Hoo, C. S. Molecules and linerly ordered ideals of MV-algebras.. Publicacions Matemàtiques, Tome 41 (1997) pp. 455-465. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41313/