Noetherian and Artinian Lattices
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Abstract
It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.
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Keywords
Artinian, Modular lattice, Lattice theory, Study of properties and structures of commutative rings, Lattice theory, Organic chemistry, Noetherian, Fuzzy Logic and Residuated Lattices, Semisimple module, QA1-939, FOS: Mathematics, Noncommutative ring, Model Theory and Topological Dynamics, Algebra over a field, Algebra and Number Theory, Artinian, Pure mathematics, Ring (chemistry), Discrete mathematics, Modular lattice, Chemistry, Computational Theory and Mathematics, Artinian ring, Physical Sciences, Computer Science, O-Minimal Structures, Geometry and Topology, Mathematics
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01 natural sciences, 0101 mathematics
Citation
Keskin Tütüncü, D. Toksoy, S. E. and Tribak, R. (2012). Noetherian and Artinian lattices. International Journal of Mathematics and Mathematical Sciences, 2012. doi:10.1155/2012/157169
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2012
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1
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8
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