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The descending chain condition in modular lattices
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Zeitschriftentitel: | Journal of the Australian Mathematical Society |
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Personen und Körperschaften: | |
In: | Journal of the Australian Mathematical Society, 14, 1972, 4, S. 443-444 |
Format: | E-Article |
Sprache: | Englisch |
veröffentlicht: |
Cambridge University Press (CUP)
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Schlagwörter: |
author_facet |
Newman, Thomas G. Newman, Thomas G. |
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author |
Newman, Thomas G. |
spellingShingle |
Newman, Thomas G. Journal of the Australian Mathematical Society The descending chain condition in modular lattices General Earth and Planetary Sciences General Environmental Science |
author_sort |
newman, thomas g. |
spelling |
Newman, Thomas G. 0004-9735 Cambridge University Press (CUP) General Earth and Planetary Sciences General Environmental Science http://dx.doi.org/10.1017/s1446788700011071 <jats:p>In a recent paper Kovács [1] studied join-continuous modular lattices which satisfy the following conditions: (i) <jats:italic>every element is a join of finitely many join-irredicibles</jats:italic>, and, (ii) <jats:italic>the set of join-irreducibles satisfies the descending chain condition</jats:italic>. He was able to prove that such a lattice must itself satisfy the descending chain condition. Interest was expressed in whether or not one could obtain the same result without the assumption of modularity and/or of join-continuity. In this paper we give an elementary proof of this result without the assumption of join- continuity (which of course must then follow as a consequence of the descending chain condition). In addition we give a suitable example to show that modularity may not be omitted in general.</jats:p> The descending chain condition in modular lattices Journal of the Australian Mathematical Society |
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Cambridge University Press (CUP), 1972 |
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Cambridge University Press (CUP), 1972 |
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1972 |
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Cambridge University Press (CUP) |
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series |
Journal of the Australian Mathematical Society |
source_id |
49 |
title |
The descending chain condition in modular lattices |
title_unstemmed |
The descending chain condition in modular lattices |
title_full |
The descending chain condition in modular lattices |
title_fullStr |
The descending chain condition in modular lattices |
title_full_unstemmed |
The descending chain condition in modular lattices |
title_short |
The descending chain condition in modular lattices |
title_sort |
the descending chain condition in modular lattices |
topic |
General Earth and Planetary Sciences General Environmental Science |
url |
http://dx.doi.org/10.1017/s1446788700011071 |
publishDate |
1972 |
physical |
443-444 |
description |
<jats:p>In a recent paper Kovács [1] studied join-continuous modular lattices which satisfy the following conditions: (i) <jats:italic>every element is a join of finitely many join-irredicibles</jats:italic>, and, (ii) <jats:italic>the set of join-irreducibles satisfies the descending chain condition</jats:italic>. He was able to prove that such a lattice must itself satisfy the descending chain condition. Interest was expressed in whether or not one could obtain the same result without the assumption of modularity and/or of join-continuity. In this paper we give an elementary proof of this result without the assumption of join- continuity (which of course must then follow as a consequence of the descending chain condition). In addition we give a suitable example to show that modularity may not be omitted in general.</jats:p> |
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author | Newman, Thomas G. |
author_facet | Newman, Thomas G., Newman, Thomas G. |
author_sort | newman, thomas g. |
container_issue | 4 |
container_start_page | 443 |
container_title | Journal of the Australian Mathematical Society |
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description | <jats:p>In a recent paper Kovács [1] studied join-continuous modular lattices which satisfy the following conditions: (i) <jats:italic>every element is a join of finitely many join-irredicibles</jats:italic>, and, (ii) <jats:italic>the set of join-irreducibles satisfies the descending chain condition</jats:italic>. He was able to prove that such a lattice must itself satisfy the descending chain condition. Interest was expressed in whether or not one could obtain the same result without the assumption of modularity and/or of join-continuity. In this paper we give an elementary proof of this result without the assumption of join- continuity (which of course must then follow as a consequence of the descending chain condition). In addition we give a suitable example to show that modularity may not be omitted in general.</jats:p> |
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id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9zMTQ0Njc4ODcwMDAxMTA3MQ |
imprint | Cambridge University Press (CUP), 1972 |
imprint_str_mv | Cambridge University Press (CUP), 1972 |
institution | DE-D161, DE-Zwi2, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1 |
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publisher | Cambridge University Press (CUP) |
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series | Journal of the Australian Mathematical Society |
source_id | 49 |
spelling | Newman, Thomas G. 0004-9735 Cambridge University Press (CUP) General Earth and Planetary Sciences General Environmental Science http://dx.doi.org/10.1017/s1446788700011071 <jats:p>In a recent paper Kovács [1] studied join-continuous modular lattices which satisfy the following conditions: (i) <jats:italic>every element is a join of finitely many join-irredicibles</jats:italic>, and, (ii) <jats:italic>the set of join-irreducibles satisfies the descending chain condition</jats:italic>. He was able to prove that such a lattice must itself satisfy the descending chain condition. Interest was expressed in whether or not one could obtain the same result without the assumption of modularity and/or of join-continuity. In this paper we give an elementary proof of this result without the assumption of join- continuity (which of course must then follow as a consequence of the descending chain condition). In addition we give a suitable example to show that modularity may not be omitted in general.</jats:p> The descending chain condition in modular lattices Journal of the Australian Mathematical Society |
spellingShingle | Newman, Thomas G., Journal of the Australian Mathematical Society, The descending chain condition in modular lattices, General Earth and Planetary Sciences, General Environmental Science |
title | The descending chain condition in modular lattices |
title_full | The descending chain condition in modular lattices |
title_fullStr | The descending chain condition in modular lattices |
title_full_unstemmed | The descending chain condition in modular lattices |
title_short | The descending chain condition in modular lattices |
title_sort | the descending chain condition in modular lattices |
title_unstemmed | The descending chain condition in modular lattices |
topic | General Earth and Planetary Sciences, General Environmental Science |
url | http://dx.doi.org/10.1017/s1446788700011071 |