| dc.contributor.author | Kalauch, Anke | |
| dc.contributor.author | Malinowski, Helena | |
| dc.date.accessioned | 2018-09-03T07:29:01Z | |
| dc.date.available | 2018-09-03T07:29:01Z | |
| dc.date.issued | 2019 | |
| dc.identifier.citation | Kalauch, A. & Malinowski, H. 2019. Vector lattice covers of ideals and bands in pre-Riesz spaces. Quaestiones mathematicae, 42(7):919-937. [https://doi.org/10.2989/16073606.2018.1501620] | en_US |
| dc.identifier.issn | 1607-3606 | |
| dc.identifier.issn | 1727-933X (Online) | |
| dc.identifier.uri | http://hdl.handle.net/10394/30872 | |
| dc.identifier.uri | https://www.tandfonline.com/doi/abs/10.2989/16073606.2018.1501620 | |
| dc.identifier.uri | https://doi.org/10.2989/16073606.2018.1501620 | |
| dc.description.abstract | Pre-Riesz spaces are ordered vector spaces which can be orde
r densely
embedded into vector lattices, their so-called vector latt
ice covers. Given a
vector lattice cover
Y
for a pre-Riesz space
X
, we address the question how
to find vector lattice covers for subspaces of
X
, such as ideals and bands. We
provide conditions such that for a directed ideal
I
in
X
its smallest extension
ideal in
Y
is a vector lattice cover. We show a criterion for bands in
X
and
their extension bands in
Y
as well. Moreover, we state properties of ideals
and bands in
X
which are generated by sets, and of their extensions in
Y | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Taylor & Francis | |
| dc.subject | Order ideal | |
| dc.subject | Band | |
| dc.subject | Pre-Riesz space | |
| dc.subject | Ordered vector space | |
| dc.subject | Vector lattice cover | |
| dc.subject | Order dense | |
| dc.subject | Extension ideal | |
| dc.subject | Extension band | |
| dc.subject | Pervasive | |
| dc.title | Vector lattice covers of ideals and bands in pre-Riesz spaces | en_US |
| dc.type | Article | en_US |
| dc.contributor.researchID | 31579922 - Malinowski, Helena | |
