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Bases and closures under infinite sums
- Source :
-
Linear Algebra & its Applications . Oct2011, Vol. 435 Issue 8, p2007-2018. 12p. - Publication Year :
- 2011
-
Abstract
- Abstract: Motivated by work of Diestel and Kühn on the cycle spaces of infinite graphs we study the ramifications of allowing infinite sums in a module . We show that every generating set in this setup contains a basis if the ground set M is countable, but not necessarily otherwise. Given a family , we determine when the infinite-sum span of is closed under infinite sums, i.e.when . We prove that this is the case if R is a field or a finite ring and each element of M lies in the support of only finitely many elements of . This is, in a sense, best possible. We finally relate closures under infinite sums to topological closures in the product space . [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 435
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 61259237
- Full Text :
- https://doi.org/10.1016/j.laa.2011.03.029