[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2014.51.1.253

MODULES WHOSE CLASSICAL PRIME SUBMODULES ARE INTERSECTIONS OF MAXIMAL SUBMODULES

Arabi-Kakavand, Marzieh (Department of Mathematical Sciences Isfahan University of Technology)
Behboodi, Mahmood (Department of Mathematical Sciences Isfahan University of Technology, School of Mathematics Institute for Research in Fundamental Sciences (IPM))

Publication Information

Bulletin of the Korean Mathematical Society / v.51, no.1, 2014 , pp. 253-266 More about this Journal

Abstract

Commutative rings in which every prime ideal is an intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that classical prime submodules are intersections of maximal submodules. It is shown that all co-semisimple modules as well as all Artinian modules are classical Hilbert modules. Also, every module over a zero-dimensional ring is classical Hilbert. Results illustrating connections amongst the notions of classical Hilbert module and Hilbert ring are also provided. Rings R over which all modules are classical Hilbert are characterized. Furthermore, we determine the Noetherian rings R for which all finitely generated R-modules are classical Hilbert.

Keywords

Hilbert ring; Hilbert module; classical prime submodule;

Citations & Related Records

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