11961

10969

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

نه، [71]ص.: مصور

ص. ع. به فارسي و انگليسي

واژه نامه

1395/10/12

كتابنامه

علوم رياضي

رياضي

ID10969

Avoiding modules co avoiding modules Goldie dimension and its dual MohammadMatin Khorshidifar m khorshidifar@math iut ac ir m khorshidifar@gmail com 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir Advisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir 2010 MSC 16P60 16D10 Keywords Avoiding modules Co avoiding modules Goldie dimension Dual Goldie dimension AbstractA module is called a uniform module if the intersection of any two non zero submodules is non zero This is equivalent to saying that every non zero submodule of M is an essential submodule Goldieused the notion of uniform modules to construct a measure of dimension for modules now knownas the Goldie dimension of a module Goldie dimension generalizes some but not all aspects of thenotion of the dimension of a vector space Finite Goldie dimension was a key assumption for severaltheorems by Goldie including Goldie s theorem which characterizes which rings are right orders in asemisimple ring Modules of nite Goldie dimension generalize both artinian modules and noetherianmodules A module M is said to have nite Goldie dimension if there is a monomorphism from a nite direct sum of uniform submodules of M to M such that the image is essential in M It is knownthat Goldie dimension of a module M is the supremum of the cardinality of independent family ofsubmodules of M A non zero module M is said to be hollow if every proper submodule is smallin M and M is said to have nite dual Goldie dimension or nite hollow dimension if there is anepimorphism with a small kernel from M to a nite direct sum of non zero hollow factor modules Itcan be shown that in this case there is a number n such that M does not allow an epimorphism toa direct sum with more than n summands We denote this by co dim M n and call co dim M thedual Goldie dimension of M Let R be a ring An R module M is said to be nitely co generated if for any family Ni i I of submodules M with i I Ni 0 there is a nite subset J I with

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