TAILIEUCHUNG - Frontiers in Mathematics

Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not finite-dimensional ([8, page 155], [32, page V]). Von Neumann proved ([32, Theorem , page 208], [8, page 162]): Every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. The book of . Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]). In abelian group theory the interest lay in determining those groups whose endomorphism rings were. | Friedrich Kasch Adolf Mader Regularity and Substructures Hom Frontiers in Mathematics BIRKHAUSER Frontiers in Mathematics Advisory Editorial Board Leonid Bunimovich Georgia Institute of Technology Atlanta USA Benoĩt Perthame Ecole Normale Supérieure Paris France Laurent Saloff-Coste Cornell University Rhodes Hall USA Igor Shparlinski Macquarie University New South Wales Australia Wolfgang Sprossig TU Bergakademie Freiberg Germany Cédric Villani Ecole Normale Supérieure Lyon France

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