Titlebook: Lattice Concepts of Module Theory; Grigore C?lug?reanu Book 2000 Springer Science+Business Media Dordrecht 2000 Group theory.Lattice.algeb

ectropion

標準

鉤針織物

Socle. Torsion lattices,Let . be a lattice with zero.

Contend

Independence. Semiatomic lattices,A subset {..}. of non-zero elements of a complete lattice . (with 0) is called . if for every . the equality . holds. In this case we use the notation . and we call this join a ..

故意

吹牛者

Lattices of finite uniform dimension,An element . is called . (or . [33]) if for every . the following implication holds: 0 < . ≤ ., 0 < . ≤ . ? . ≠ 0 (i.e., all non-zero elements from ./0 are essential in ./0).

會議

安撫

Coatomic lattices,The interest in coatomic lattices goes back to H. Bass [2] (in 1960) who defined B-objects, i.e., modules . such that every submodule . is contained in a maximal submodule.

反饋

,Co—compact lattices,A complete lattice . is called . (or . in [34]) if for every subset . of . such that Λ . = 0 there is a finite subset . of . such that Λ . 0. Obviously, . is co—compact if and only if the dual L° is compact. An element a ∈ . is called . if the sublattice ./0 is co—compact.

敲詐

Supplemented lattices. Locally artinian lattices,For the beginning we mention (a straightforward lattice version of [41]) some simple results about supplements and supplemented lattices.