حول فضاء الموديلات الجزئية العظمى == On The Space Of Maximal Submodules
Author name:
ايمان يحيى حبيب
Supervisor name:
حبيب كريم عبد الله
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Kufa - College Of Education For Girls - Department Of Mathematics
Language:
English
University location:
Najaf
First pages:
27T351 - p.pdf
Abstract:
Let R be a commutative ring with identity and M be a module over R . The set of all maximal submodules of M is denoted by Max(M) . The Rmodule M is said to be a M - top R - module if Max(M) has a Zariski topology .The main purpose of this thesis, is to study when Zariski topology on Max(M) exists and study the relationship between the topological properties of the space Max(M) and the topological properties of an Rmodule M . In addition, the compactness , connectedness , strongly connectedness , locally compact , locally connected , HK - space and the separation axioms will be shown .From the main results which have been got , if M is a multiplication faithful finitely generated R - module, then Max(M) and Max(R) are homeomorphic . Also the study will prove if M is a multiplication Rmodule then M is semi - local if and only if Max(M) is an HK - space . Moreover , it would be proved that if M is a multiplication Rmodule , then M is semi - simple if and only if Max(M) is a disconnected space under a certain condition .Also , it would be stated that for any M - top R - module , M is a local module if and only if Max(M) is strongly connected .Also , it would be proved that for a multiplication R - module , if M is an F - regular ,then Max(M) is a regular space .
