## $a^*$-closures of lattice-ordered groups

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- by Roger Bleier and Paul Conrad PDF
- Trans. Amer. Math. Soc.
**209**(1975), 367-387 Request permission

## Abstract:

A convex $l$-subgroup of an $l$-group $G$ is*closed*if it contains the join of each of its subsets that has a join in $G$. An extension of $G$ which preserves the lattice of closed convex $l$-subgroups of $G$ is called an ${a^ \ast }$

*-extension*of $G$. In this paper we consider ${a^ \ast }$-extensions and ${a^ \ast }$-closures of $G$.

## References

- Garrett Birkhoff,
*Lattice theory*, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR**0227053**
A. Bigard, - Roger D. Bleier,
*The SP-hull of a lattice-ordered group*, Canadian J. Math.**26**(1974), 866–878. MR**345891**, DOI 10.4153/CJM-1974-081-x - Roger Bleier and Paul Conrad,
*The lattice of closed ideals and $a^{\ast }$-extensions of an abelian $l$-group*, Pacific J. Math.**47**(1973), 329–340. MR**325486**, DOI 10.2140/pjm.1973.47.329 - J. W. Brewer, P. F. Conrad, and P. R. Montgomery,
*Lattice-ordered groups and a conjecture for adequate domains*, Proc. Amer. Math. Soc.**43**(1974), 31–35. MR**332616**, DOI 10.1090/S0002-9939-1974-0332616-X - Richard D. Byrd,
*Complete distributivity in lattice-ordered groups*, Pacific J. Math.**20**(1967), 423–432. MR**207866**, DOI 10.2140/pjm.1967.20.423 - Richard D. Byrd and Justin T. Lloyd,
*Closed subgroups and complete distributivity in lattice-ordered groups*, Math. Z.**101**(1967), 123–130. MR**218284**, DOI 10.1007/BF01136029 - Donald A. Chambless,
*Representation of the projectable and strongly projectable hulls of a lattice-ordered group*, Proc. Amer. Math. Soc.**34**(1972), 346–350. MR**295990**, DOI 10.1090/S0002-9939-1972-0295990-7 - Paul Conrad,
*The essential closure of an Archimedean lattice-ordered group*, Duke Math. J.**38**(1971), 151–160. MR**277457** - Paul Conrad,
*The hulls of representable $l$-groups and $f$-rings*, J. Austral. Math. Soc.**16**(1973), 385–415. Collection of articles dedicated to the memory of Hanna Neumann, IV. MR**0344173**, DOI 10.1017/S1446788700015391
—, - Paul Conrad,
*On ordered division rings*, Proc. Amer. Math. Soc.**5**(1954), 323–328. MR**61582**, DOI 10.1090/S0002-9939-1954-0061582-7 - L. Fuchs,
*Partially ordered algebraic systems*, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR**0171864** - A. M. W. Glass and W. Charles Holland (eds.),
*Lattice-ordered groups*, Mathematics and its Applications, vol. 48, Kluwer Academic Publishers Group, Dordrecht, 1989. Advances and techniques. MR**1036072**, DOI 10.1007/978-94-009-2283-9
S. Wolfenstein, - Charles Holland,
*Extensions of ordered groups and sequence completion*, Trans. Amer. Math. Soc.**107**(1963), 71–82. MR**146273**, DOI 10.1090/S0002-9947-1963-0146273-6

*Contribution a la théorie des groupes reticules*, Thesis, University of Paris, 1969.

*Lattice-ordered groups*, Tulane University, New Orleans, La., 1970.

*Contribution à l’étude des groupes reticulés; extensions archimédiennes, groupes à valeurs normales*, Thesis, University of Paris, 1970. R. Ball, Ph. D. Thesis, University of Wisconsin, Madison, Wis., 1974.

## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**209**(1975), 367-387 - MSC: Primary 06A55
- DOI: https://doi.org/10.1090/S0002-9947-1975-0404087-1
- MathSciNet review: 0404087