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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.