Derya Keskı̇n Tütüncü, Sultan Eylem Toksoy, Rachid Trıbak
Abstract
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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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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.
Key concepts: Mathematics, Artinian ring, Semisimple module, Noetherian, Pure mathematics, Discrete mathematics, Algebra over a field, Noncommutative ring