Open AccessNoetherian and Artinian Lattices
Author(s) -
Derya Keskı̇n Tütüncü,
Sultan Eylem Toksoy,
Rachid Trıbak
Publication year - 2012
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/2012/157169
Subject(s) - mathematics , artinian ring , semisimple module , noetherian , pure mathematics , discrete mathematics , algebra over a field , noncommutative ring , ring (chemistry) , chemistry , organic chemistry
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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