A problem of annihilator primes in MV-algebras (Q1025063)

In his paper ``Interpretation of AF \(C^*\)-algehras in Łukasiewiez sentential calculus'' [J. Funct. Anal. 65, 15--63 (1986; Zbl 0597.46059)], the present reviewer introduced a categorical equivalence \(\Gamma\) between abelian unital lattice-ordered groups and MV-algebras -- the algebras of Łukasiewicz infinite-valued logic. In the paper under review, the author uses this functor to generalize a result of Cignoli and Torrens concerning the poset of prime ideals of a unital lattice-ordered abelian group. The author also characterizes those MV-algebras where every prime ideal is the annihilator of a linearly ordered ideal, thus giving a negative answer to a problem of \textit{L. P. Belluce} [Can. J. Math. 38, 1356--1379 (1986; Zbl 0625.03009)].