On some classes of modules and characterization of rings

ABSTRACT

An abstract class of R-Mod is termed Additive Class if it is closed under taking submodules, homomorphic images and finite direct sums. In this paper we study the lattice properties of R-ad, the big lattice of all additive classes in R-mod for R any ring. Also, we study the lattice properties of R-ad when R is a Noetherian or semisimple ring. We describe a characterization of some rings through the additive classes and their properties. We study some properties of additive classes related with the associated linear filters.

KEYWORDS:

• Additive classes
• big lattices
• linear filters

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16D80
• 16D60
• 16P40

Acknowledgments

The second author is supported by a scholarship from CONACyT Mexico. The authors wish to thank the referee for the useful suggestions on the writing of this paper.