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A characterization of non-removable ideals in commutative locally multiplicatively pseudoconvex algebras

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Abstract

We introduce here the concept of weak joint topological divisors of zero in commutative locally multiplicatively pseudoconvex Hausdorff algebras and use it for the characterization of non-removable ideals in these algebras. Examples of removable and non-removable ideals in these algebras are given.

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Notes

  1. When every element of this base is convex and idempotent, \(A\) is called \(m\)-convex.

  2. Only the commutative case will be considered in this paper.

  3. A subset of seminorms \(S\subset P(A)\) will be called cofinal if for each \(p\) in \(P(A)\) there exists \(p^{\prime }\) in \(P(A)\) such that \(p\preceq p^{\prime }\). Clearly, any cofinal set of seminorms gives the topology of \(A\).

  4. This can be treated as a generalization of Theorem 1 in [6] and as a refinement of Theorem 1 in [11].

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, 2, J. Liivi Str., room 614, 50409 , Tartu, Estonia

    Mati Abel

  2. Mathematical Institute, Polish Academy of Sciences, Śniadeckich 8, P. O. Box 21, 00-95 , Warsaw, Poland

    Wiesław Żelazko

Authors
  1. Mati Abel
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  2. Wiesław Żelazko
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Correspondence to Mati Abel.

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Abel, M., Żelazko, W. A characterization of non-removable ideals in commutative locally multiplicatively pseudoconvex algebras. Rend. Circ. Mat. Palermo 62, 179–187 (2013). https://doi.org/10.1007/s12215-012-0100-8

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  • DOI: https://doi.org/10.1007/s12215-012-0100-8

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