Topological algebras with maximal regular ideals closed

Mati Abel

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1054-1059
  • ISSN: 2391-5455

Abstract

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It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.

How to cite

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Mati Abel. "Topological algebras with maximal regular ideals closed." Open Mathematics 10.3 (2012): 1054-1059. <http://eudml.org/doc/269677>.

@article{MatiAbel2012,
abstract = {It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.},
author = {Mati Abel},
journal = {Open Mathematics},
keywords = {Topological algebra; von Neumann bornology; Closedness of maximal ideals; topological algebra; closedness of maximal ideals},
language = {eng},
number = {3},
pages = {1054-1059},
title = {Topological algebras with maximal regular ideals closed},
url = {http://eudml.org/doc/269677},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Mati Abel
TI - Topological algebras with maximal regular ideals closed
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1054
EP - 1059
AB - It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.
LA - eng
KW - Topological algebra; von Neumann bornology; Closedness of maximal ideals; topological algebra; closedness of maximal ideals
UR - http://eudml.org/doc/269677
ER -

References

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