caa a22 4500 445835613 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00209-010-0687-4 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0687-4 PID pairs of rings and maximal non-PID subrings [Elektronische Daten] [Ahmed Ayache, Mabrouk Ben Nasr, Noômen Jarboui] For a ring extension $${R \subset S, \,(R, S)}$$ is called a principal ideal domain pair (for short PID pair) if every domain $${T, \,R \subseteq T \subseteq S}$$ , is a principal ideal domain. When R is a field it is shown that (R, S) is a PID pair iff S is algebraic over R. When R is not a field it is proved that the only PID pairs are those such that R is a PID and S is an overring of R. The second purpose of this paper is to study maximal non-PID subrings. We characterize these type of rings. Further applications and results are also presented. Springer-Verlag, 2010 Principal ideal domain nationallicence Dedekind domain nationallicence Prüfer domain nationallicence Pullback nationallicence Residually algebraic extension nationallicence Ayache Ahmed Department of Mathematics, Faculty of Science, University of Bahrain, P.O. Box 32038, Sukhir, Kingdom of Bahrain aut Ben Nasr Mabrouk Department of Mathematics, Faculty of Science, King Faisal University, P.O. Box 380, 31982, Al-Hassa, Kingdom of Saudi Arabia aut Jarboui Noômen Department of Mathematics, Faculty of Science, King Faisal University, P.O. Box 380, 31982, Al-Hassa, Kingdom of Saudi Arabia aut Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 635-647 0025-5874 268:3-4<635 2011 268 209 https://doi.org/10.1007/s00209-010-0687-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0687-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ayache Ahmed Department of Mathematics, Faculty of Science, University of Bahrain, P.O. Box 32038, Sukhir, Kingdom of Bahrain aut NATIONALLICENCE 700 1- Ben Nasr Mabrouk Department of Mathematics, Faculty of Science, King Faisal University, P.O. Box 380, 31982, Al-Hassa, Kingdom of Saudi Arabia aut NATIONALLICENCE 700 1- Jarboui Noômen Department of Mathematics, Faculty of Science, King Faisal University, P.O. Box 380, 31982, Al-Hassa, Kingdom of Saudi Arabia aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 635-647 0025-5874 268:3-4<635 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer