Regularity and substructures of hom

Autori

• Friedrich Kasch

Parametri

• 164 pagine
• 6 ore di lettura

• Matematica

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Regular rings were introduced by John von Neumann to clarify aspects of operator algebras. A continuous geometry is an indecomposable, continuous, complemented modular lattice that is not finite-dimensional. Von Neumann proved that every continuous geometry is isomorphic to the lattice of right ideals of some regular ring. K. R. Goodearl's work provides an extensive account of various types of regular rings, while several papers have explored modules over these rings. In abelian group theory, researchers aimed to identify groups whose endomorphism rings were regular or had related properties. Brown and McCoy introduced an interesting feature, demonstrating that every ring contains a unique largest ideal with all regular elements. These studies highlighted the close relationship between regularity and direct sum decompositions. Ware and Zelmanowitz defined regularity in modules and investigated the structure of regular modules, while Nicholson generalized the notion and theory of regular modules. This algebraic monograph explores a generalization of regularity to the homomorphism group of two modules, introduced by the first author. The text requires minimal background and is accessible to students familiar with standard modern algebra. The focus is on right unital R-modules.

Lingua: Inglese

Pubblicato: 2009

(In brossura)