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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2005, Number 2, Pages 43–50
(Mi basm126)
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This article is cited in 2 scientific papers (total in 2 papers)
On the lattice of closed classes of modules
A. I. Kashu Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
Abstract:
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 ${\EuScript K}\in R$-cl its pseudocomplement ${\EuScript K}^*$ in $R$-cl is characterized. The skeleton of $R$-cl (i.e. the set of classes of the form ${\EuScript K}^*$, ${\EuScript K}\in R$-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.
Keywords and phrases:
Closed class of modules, natural class, frame (Brouwerian lattice), pseudocomplement, boolean lattice.
Received: 21.07.2005
Citation:
A. I. Kashu, “On the lattice of closed classes of modules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, no. 2, 43–50
Linking options:
https://www.mathnet.ru/eng/basm126 https://www.mathnet.ru/eng/basm/y2005/i2/p43
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Abstract page: | 238 | Full-text PDF : | 68 | References: | 34 | First page: | 1 |
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