zbMATH — the first resource for mathematics

MV-algebras, ideals and semisimplicity. (English) Zbl 0677.03041
The author proves more generally some results of L. P. Belluce on MV- algebras. He characterizes implicative maximal ideals and implicative prime ideals. He proves that i) if a linearly ordered ideal has no atoms, then for each \(x\neq 0\) in the ideal and each \(n>0\) it is possible to find an element \(y\neq 0\) in the ideal such that ny\(\leq x\); also ii) a linearly ordered algebra which contains no atoms is densely ordered. These are generalizations of results of C. C. Chang.
Reviewer: M.Abad

03G10 Logical aspects of lattices and related structures
03B50 Many-valued logic
06D99 Distributive lattices
06B15 Representation theory of lattices
06B10 Lattice ideals, congruence relations