Title of article
THE LOEWY SERIES OF AN FCP (DISTRIBUTIVE) RING EXTENSION
Author/Authors
Picavet, Gabriel Mathematiques - 8 Rue du Forez 63670 Le Cendre, France , Picavet-L’Hermitte, Martine Mathematiques - 8 Rue du Forez 63670 Le Cendre, France
Pages
35
From page
15
To page
49
Abstract
t. If R ⊆ S is an extension of commutative rings, we consider the lattice ([R, S], ⊆) of all the R-subalgebras of S. We assume that the poset [R, S]
is both Artinian and Noetherian; that is, R ⊆ S is an FCP extension. The
Loewy series of such lattices are studied. Most of main results are gotten in
case these posets are distributive, which occurs for integrally closed extensions.
In general, the situation is much more complicated. We give a discussion for
finite field extensions.
Keywords
FIP , FCP extension , minimal extension , support of a module , distributive lattice , Boolean lattice , atom , socle , Loewy series , Galois extension
Journal title
International Electronic Journal of Algebra
Serial Year
2021
Full Text URL
Record number
2596703
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