We say that a subset X of a left R-module M is weakly independent provided that whenever
a 1 x 1+⋯+ anxn= 0 for pairwise distinct elements x 1,…, xn form X, then none of a 1,…, an is …

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A weak basis of a module is a generating set of the module minimal with respect to
inclusion. A module is said to be regularly weakly based provided that each of its generating …

We characterize Abelian groups with a minimal generating set: Let τ A denote the maximal
torsion subgroup of A. An infinitely generated Abelian group A of cardinality κ has a minimal …

Projective covers and minimal sets of generators over local rings - ScienceDirect Skip to main
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For a right vector space we study the question whether any generating set of subspaces of a
bounded finite dimension contains a generating subset minimal with respect to inclusion …

The problem of generation and oneness considered for expressing about an element is very
important and has a big effect in mathematics in general and in algebra in special for …

Title: Modules with a minimal generating set Author: Michal Hrbek Department: Department
of Algebra Supervisor: Mgr. Pavel Růžička, Ph. D., Department of Algebra Abstract: By a …

We study a question whether a generating set of subspaces of a right vector space of a
bounded finite dimension contains a generating subset minimal with respect to inclusion …

We find some sufficient conditions under which the permutational wreath product of two
groups has a minimal generating set. In particular we prove that for a regular rooted tree the …