Convex subalgebras of upper bounded GMV-algebras (Q2822861)

The paper deals with generalized MV-algebras (= GMV-algebras) in the sense of \textit{N. Galatos} and \textit{C. Tsinakis} [J. Algebra 283, No. 1, 254--291 (2005; Zbl 1063.06008)]. It is known that every upper bounded GMV-algebra \(M\) can be constructed using a pair \({\mathbf L}=(G_1,L)\), where \(G_1\) is an \(\ell \)-group and \(L\) is a lattice filter of the negative cone \(G_1^-\) satisfying certain properties. The author proves that the systems of all convex subgroups of \(G_1\) and of all convex subalgebras of \({\mathbf L}\) are equivalent. The similar is proved for the corresponding systems of ideals. Moreover, he describes the particular case of pseudo MV-algebras.