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Volume :25 Issue : 2 1998      Add To Cart                                                                    Download

Some conditions for a Q-lattice or a Laskerian lattice to be Noetherian

Auther : H. M. NAKKAR AND E. A. AL-KHOUJA

 Department of Mathematics, Faculty of Sciences, University of Aleppo, Aleppo, Syria

  ABSTRACT

A Q-lattice (Laskerian lattice) is a multiplicative lattice in which every element x I is a finite.-... L: rsection) of  primary elements. It is well known that a Q-lattice or a Laskerian lattice need not be Noetherian.

The purpose of this paper is to give some conditions for a Q-lattice or a Laskerian lattice to hr U ‘We show that if L is a Q-lattice and a R-lattice locally Noetherian, then L is Noetherian. We also prove that if L is a R-modular Laskerian lattice and for every prime element P of L the maximal element of Lp (the localization of L at p) is finitely generated, then L is Noetherian .  

Keywords: Lattice modules; multiplicative lattice; primary element

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