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Ultima descărcare din IBN: 2022-03-28 17:51 |
SM ISO690:2012 KASHU, A.. On the lattice of closed classes of modules. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2005, nr. 2(48), pp. 43-50. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 2(48) / 2005 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 43-50 | ||||||
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Rezumat | ||||||
The family of closed classes of left R-modules R-cl (i.e. of classes which
can be described by sets of left ideals of R) is transformed in a lattice and its properties are studied. The lattice R-cl is a frame (or Brouwerian lattice, or Heyting algebra). For every class K ∈ R-cl its pseudocomplement K* in R-cl is characterized. The skeleton of R-cl (i.e. the set of classes of the form K*, K ∈ R-cl) coincides with the
boolean lattice R-nat of natural classes of R-Mod. In parallels the isomorphic with
R-cl lattice R-Cl of closed sets of left ideals of R is investigated, exposing some similar
properties. |
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Cuvinte-cheie Closed class of modules, Natural class, frame (Brouwerian lattice), pseudocomplement, boolean lattice. |
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