naa a22 4500 510736769 CHVBK 20180411083013.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s13366-012-0101-y doi (NATIONALLICENCE)springer-10.1007/s13366-012-0101-y Jaballah Ali Department of Mathematics, College of Sciences, Univesity of Sharjah, Sharjah, UAE aut Graph theoretic characterizations of maximal non-valuation subrings of a field [Elektronische Daten] [Ali Jaballah] We establish several new characterizations of maximal non-valuation subrings of a field involving several concepts of commutative algebra related to the set of prime ideals and the set of overrings. For example we show that an integral domain R of finite dimension d is a maximal non-valuation subring of a field if, and only if R is either integrally closed with a set of overrings isomorphic to a kite-graph of dimension d+1, or is non-integrally closed with a chained set of overrings of dimension d+1. The Managing Editors, 2012 Quasilocal ring nationallicence Semiquasilocal ring nationallicence Integral domain nationallicence Krull dimension nationallicence Equidimensional nationallicence Ring extension nationallicence Intermediate ring nationallicence Overring nationallicence Integral extension nationallicence Integrally closed nationallicence Valuation domain nationallicence Prüfer domain nationallicence QR -domain nationallicence QQR -domain nationallicence Chain nationallicence Antichain nationallicence Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 111-120 0138-4821 54:1<111 2013 54 13366 https://doi.org/10.1007/s13366-012-0101-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0101-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jaballah Ali Department of Mathematics, College of Sciences, Univesity of Sharjah, Sharjah, UAE aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 111-120 0138-4821 54:1<111 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer