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Interior Operators Generated by Ideals in Complete Domains

Author

Listed:
  • Dănuţ Rusu

    (Faculty of Mathematics, Alexandru Ioan Cuza University, 700506 Iaşi, Romania)

  • Gabriel Ciobanu

    (Facutly of Computer Science, Alexandru Ioan Cuza University, 700506 Iaşi, Romania)

Abstract

This article presents some properties of a special class of interior operators generated by ideals. The mathematical framework is given by complete domains, namely complete posets in which the set of minimal elements is a basis. The first part of the paper presents some preliminary results; in the second part we present the novel interior operator denoted by G ( i , I ) , an operator built starting from an interior operator i and an ideal I . Various properties of this operator are presented; in particular, the connection between the properties of the ideal I and the properties of the operator G ( i , I ) . Two such properties (denoted by P i and Q i ) are extensively analyzed and characterized. Additionally, some characterizations for compact elements are presented.

Suggested Citation

  • Dănuţ Rusu & Gabriel Ciobanu, 2021. "Interior Operators Generated by Ideals in Complete Domains," Mathematics, MDPI, vol. 9(16), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1911-:d:612336
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