A characterization of commutative Fréchet algebras with all ideals closed

W. Żelazko

Studia Mathematica (2000)

  • Volume: 138, Issue: 3, page 293-300
  • ISSN: 0039-3223

Abstract

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Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra

How to cite

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Żelazko, W.. "A characterization of commutative Fréchet algebras with all ideals closed." Studia Mathematica 138.3 (2000): 293-300. <http://eudml.org/doc/216707>.

@article{Żelazko2000,
abstract = {Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra},
author = {Żelazko, W.},
journal = {Studia Mathematica},
keywords = {commutative Fréchet algebras; ideal; Noetherian algebra},
language = {eng},
number = {3},
pages = {293-300},
title = {A characterization of commutative Fréchet algebras with all ideals closed},
url = {http://eudml.org/doc/216707},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Żelazko, W.
TI - A characterization of commutative Fréchet algebras with all ideals closed
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 3
SP - 293
EP - 300
AB - Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra
LA - eng
KW - commutative Fréchet algebras; ideal; Noetherian algebra
UR - http://eudml.org/doc/216707
ER -

References

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  1. [1] M. Akkar et C. Nacir, Continuité automatique dans les limites inductives localement convexes de Q-algèbres de Fréchet, Ann. Sci. Math. Québec 19 (1995), 115-130. Zbl0840.46031
  2. [2] S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932. Zbl0005.20901
  3. [3] G. Carboni and A. Larotonda, An example of a Fréchet algebra which is a principal ideal domain, this issue, 265-275. Zbl0969.46041
  4. [4] A. V. Ferreira and G. Tomassini, Finiteness properties of topological algebras, Ann. Scuola Norm. Sup. Pisa 5 (1978), 471-488. Zbl0397.46045
  5. [5] H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer, 1971. 
  6. [6] A. Mallios, Topological Algebras. Selected Topics, North-Holland, 1986. 
  7. [7] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). Zbl0047.35502
  8. [8] S. Rolewicz, Metric Linear Spaces, PWN, 1972. 
  9. [9] H. H. Schaefer, Topological Vector Spaces, Springer, 1971. 
  10. [10] W. Żelazko, Selected Topics in Topological Algebras, Aarhus Univ. Lecture Notes 31, 1971. Zbl0221.46041
  11. [11] W. Żelazko, On maximal ideals in commutative m-convex algebras, Studia Math. 58 (1976), 291-298. Zbl0344.46103
  12. [12] W. Żelazko, On topologization of countably generated algebras, ibid. 112 (1994), 83-88. Zbl0832.46042
  13. [13] W. Żelazko, On m-convexity of commutative real Waelbroeck algebras, Comm. Math., submitted. Zbl1001.46035
  14. [14] W. Żelazko, Characterizations of Q-algebras of type F and of F-algebras with all ideals closed, Acta Comm. Univ. Tartuensis, to appear. Zbl1044.46041

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