author_facet Newman, Thomas G.
Newman, Thomas G.
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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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.
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author_sort newman, thomas g.
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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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imprint_str_mv Cambridge University Press (CUP), 1972
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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