Azarpanah, F.; Karamzadeh, O. A. S. Algebraic characterizations of some disconnected spaces. (English) Zbl 1117.54030 Ital. J. Pure Appl. Math. 12, 155-168 (2002). The authors characterize various disconnectedness properties ((strong) zero-dimensionality, basical or extremal disconnectedness) by means of ideals in \(C(X)\), mostly that they are generated by some idempotents. Another characterization: \(X\) is extremally disconnected iff \(C(X)\) is a Baer ring iff \(C^*(X)\) is a Baer ring (for P-spaces one gets regular Baer rings). Reviewer: Miroslav Hušek (Praha) Cited in 21 Documents MSC: 54C40 Algebraic properties of function spaces in general topology 16S60 Associative rings of functions, subdirect products, sheaves of rings 54D99 Fairly general properties of topological spaces 54F65 Topological characterizations of particular spaces PDFBibTeX XMLCite \textit{F. Azarpanah} and \textit{O. A. S. Karamzadeh}, Ital. J. Pure Appl. Math. 12, 155--168 (2002; Zbl 1117.54030)