Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
free lattice-ordered group; compatible sequential convergences; atom; free abelian lattice ordered group; sequential convergence
free lattice-ordered group; compatible sequential convergences; atom; free abelian lattice ordered group; sequential convergence
Summary:
In this paper the partially ordered set Conv $G$ of all sequential convergences on $G$ is investigated, where $G$ is either a free lattice ordered group or a free abelian lattice ordered group.
References:
[1] M. Anderson T. Feil: Lattice-Ordered Groups, An Introduction. Reidel Publ., Dordrecht, 1988. MR 0937703
[2] S. Bernau: Free abelian lattice groups. Math. Ann. 150(1969), 48-59. MR 0241340 | Zbl 0157.36801
[3] G. Birkhoff: Lattice Theory. Third Edition, Providence, 1967. MR 0227053 | Zbl 0153.02501
[4] P. Conrad: Free abelian l-groups and vector lattices. Math. Ann. 190 (1971), 306-312. DOI 10.1007/BF01431159 | MR 0281667
[5] P. Conrad: Free lattice-ordered groups. J. Algebra 16 (1970), 191-203. DOI 10.1016/0021-8693(70)90024-4 | MR 0270992 | Zbl 0213.31502
[6] P. Conrad: Lattice-Ordered Groups. Tulane Lecture Notes; New Orleans, 1970. Zbl 0258.06011
[7] R. Frič F. Zanolin: Sequential convergence in free groups. Rend. Ist. Matem. Univ. Trieste 18 (1986), 200-218. MR 0928331
[8] M. Harminc: Sequential convergences on abelian lattice-ordered groups. Convergence Structures 1984. Mathematical Research, Band 24, Akademie-Verlag, Berlin, 1985, pp. 153-158. MR 0835480
[9] M. Harminc: The cardinality of the system of all sequential convergences on an abelian lattice ordered group. Czechoslovak Math. J. 31 (1987), 533-546. MR 0913986
[10] M. Harminc: Sequential convergences on lattice ordered groups. Czechoslov. Math. J 39 (1989), 232-238. MR 0992130
[11] M. Harminc: Convergences on lattice ordered groups. Dissertation, Math. Inst. Slovak Acad. Sci, 1986. (In Slovak.)
[12] M. Harminc J. Jakubík: Maximal convergences and minimal proper convergences in l-groups. Czechoslov. Math. J. 39 (1989), 631-640. MR 1017998
[13] J. Jakubík: Convergences and complete distributivity of lattice ordered groups. Math. Slovaca 38 (1988), 269-272. MR 0977905
[14] J. Jakubík: Lattice ordered groups having a largest convergence. Czechoslov. Math. J. 39 (1989), 717-729. MR 1018008
[15] B. M. Koпытов: Рещеточно упорядоченные группы. Mocквa, 1984. Zbl 1063.82528
[16] J. Novák: On a free convergence group. Proc. Conf. on Convergence Structures, Lawton, Oklahoma, 1980, pp. 97-102. MR 0605123
[17] E. C. Weinberg: Free lattice-ordered abelian groups. Math. Ann. 151 (1963), 187-199. DOI 10.1007/BF01398232 | MR 0153759 | Zbl 0114.25801
[18] E. C. Weinberg: Free lattice-ordered abelian groups. II. Math. Ann. 159 (1965), 217-222. DOI 10.1007/BF01362439 | MR 0181668 | Zbl 0138.26201
Search
Partner of
