# A characterization of commutative Fréchet algebras with all ideals closed

Studia Mathematica (2000)

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

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topŻelazko, 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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- [2] S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932. Zbl0005.20901
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- [7] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). Zbl0047.35502
- [8] S. Rolewicz, Metric Linear Spaces, PWN, 1972.
- [9] H. H. Schaefer, Topological Vector Spaces, Springer, 1971.
- [10] W. Żelazko, Selected Topics in Topological Algebras, Aarhus Univ. Lecture Notes 31, 1971. Zbl0221.46041
- [11] W. Żelazko, On maximal ideals in commutative m-convex algebras, Studia Math. 58 (1976), 291-298. Zbl0344.46103
- [12] W. Żelazko, On topologization of countably generated algebras, ibid. 112 (1994), 83-88. Zbl0832.46042
- [13] W. Żelazko, On m-convexity of commutative real Waelbroeck algebras, Comm. Math., submitted. Zbl1001.46035
- [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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