Interior Operators Generated by Ideals in Complete Domains

Dănuţ Rusu and Gabriel Ciobanu
Additional contact information
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

Mathematics, 2021, vol. 9, issue 16, 1-9

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.

Keywords: directed complete partial order; compact elements; ideals in complete domains; interior operators generated by ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1911/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1911/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1911-:d:612336

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().