General distributivity and thickness of modules

Abstract

يقال أن التشكيل MR هو wthick relative إلى S إذا كان dim S < w لجميع العوامل الجزئية S لـM وS € S وw هي عدد أصل أكبر من 2 في هذا البحث ندرس التشكيلات التي تحقق A nBx n (A n Bµ) لجميع التشكيلات الجزئية A وعائلات التشكيلات الجزئية {Bx} A بحيث w IAI wthick modules كذلك درسنا خواص تشكيلات لكل من الأنواع wquasiinvariant relative wnoetherian and relative wBezout modules

Let w 2 be a cardinal and S a class of semisimple left Rmodules (closed under isomorphisms) A module RM is called wthick relative to S if dim S < w for each subfactor S of M with S € S This notion allows us to study from a unified point of view wdistributive modules i e modules satisfying A nBx n (A n Bµ) for all submodules A and families {Bx} A of submodules with cardinality IAI w and wthick modules i e modules which are wthick relative to the class of all semisimple left Rmodules In particular 2distributive modules coincide with distributive modules 2thick modules coincide with uniserial modules Nothick modules coincide with q f d modules i e modules whose factor modules have finite uniform dimension We also consider relative wquasiinvariant relative wnoetherian and relative wBezout modules Properties of modules from these classes are investigated including the relationship between them Moreover for modules RM and RU the relationship between wdistributivity of M and properties of the left End R (U) module Hom R(U M) and the right End R(U)module Hom R(M U) are studied