Hulls for various kinds of \(\alpha\)-completeness in Archimedean lattice-ordered groups (Q1970936)

Within Archimedean \(l\)-groups, and with \(\alpha\) an infinite cardinal or \(\infty\), the authors consider \(\mathbb X\)-hulls where \(\mathbb X\) stands for any of the following classes of \(l\)-groups: laterally \(\alpha\)-complete; boundedly laterally \(\alpha\)-complete, conditionally \(\alpha\)-complete; combinations of the preceding, together with divisibility and/or relative uniform completeness. All these hulls exist, and may be obtained by iterated adjunction of required extra elements, within the essential hull. A lot of results on these hull operators are established.