Hulls for various kinds of -completeness in archimedean lattice-ordered groups, Order 16 (1999) [5 citations — 3 self]
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by Anthony W. Hager, Jorge Martinez
Martinez / Journal of Pure and Applied Algebra 169 (2002) 51–69 69
http://www.math.ufl.edu/~martinez/alpha.ps
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Abstract:
Abstract. Within archimedean `{groups, and with an innite cardinal or 1, we consider X{hulls where X stands for any of the following classes of `{groups: {projectable; laterally {complete; boundedly laterally {complete; conditionally {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 the required extra elements, within the essential hull. When the `{group is relatively {complemented one step in the iteration suces for several crucial properties. We derive from the above a considerable number of equations involving combinations of these hull operators. 1
Citations
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| 14 | The essential closure of an archimedean lattice-ordered group – Conrad - 1971 |
| 9 | Category Theory, 2nd Ed – Herrlich, Strecker - 1979 |
| 8 | Algebraic extensions of an archimedean lattice-ordered group – Ball - 1993 |
| 7 | projectable and laterally -complete archimedean lattice-ordered groups – Hager - 1995 |
| 5 | The hulls of representable `-groups and f-rings – Conrad - 1973 |
| 4 | Order and disjoint completeness of linear partially ordered spaces – Veksler - 1972 |
| 2 | The lateral completion of a lattice ordered group – Bernau - 1975 |
| 2 | More on the laterally -complete re of an archimedean lattice-ordered group, Order – Hager, Martinez - 1999 |
| 1 | A new construction of the Dedekind completion of vector lattices and divisible `{groups; Siber – Veksler - 1969 |
