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مؤثرات كاما الجدائية == Multiplication Gamma Acts
Author name:
سامر عدنان جبير
Supervisor name:
مهدي صادق عباس
General topic:
Mathematics
Specific topic:
Algebra
Degree:
Doctorate
University:
Mustansiriyah University - College Of Science - Department Of Mathematics
Language:
English
University location:
Baghdad
Key words:
- Multiplication Gamma Acts
First pages:
T78183 - p.pdf
Abstract:
The main aim of this thesis is to generalize the concept of multiplication module on a set of gamma act over gamma semigroup , further many properties of gamma acts can be done in a multiplication gamma acts.
Throughout this thesis, we introduce the definition of multiplication gamma acts and some related concepts. Some characterizations of this definition are given. Also, we studied some of the properties that are satisfied on multiplication modules but not satisfied on multiplication gamma acts. Some new definitions have been illustrated including (α-divisible, large, uniform , gamma nilpotent, fully invariant and finitely cogenerated) gamma acts and their properties are clarified. For a gamma act M, we define the associated gamma ideal η(M) . We show that η(M) is a globally idempotent multiplication gamma ideal. Relation between multiplication gamma act and free gamma act was studied. Also, we define the concept of product gamma subacts of gamma act , particularly product gamma subacts of multiplication gamma act then we obtain some related results. Using our concept to introduce new mathematical system which is called the semigroup associative with multiplication gamma act and its basic properties are discussed.
Moreover , we introduce the definitions of pure and idempotent gamma subacts of multiplication gamma acts and clarified their properties . Also, we study the relation between them and a multiplication gamma act . The concept of prime gamma subact is introduce .Some results of this concept are considered . Using this concept to introduce the definition of spectrum gamma acts and investigate it's properties. Finally , we give the notion of topological gamma act and generalize this notion on a some properties of a topological space . The relation between it and(multiplication , cyclic) gamma acts is studied . Also, we introduce another topological space is called the endomorphism topology and we will prove that topological gamma act and a subspace of our topology are homeomorphic.
Throughout this thesis, we introduce the definition of multiplication gamma acts and some related concepts. Some characterizations of this definition are given. Also, we studied some of the properties that are satisfied on multiplication modules but not satisfied on multiplication gamma acts. Some new definitions have been illustrated including (α-divisible, large, uniform , gamma nilpotent, fully invariant and finitely cogenerated) gamma acts and their properties are clarified. For a gamma act M, we define the associated gamma ideal η(M) . We show that η(M) is a globally idempotent multiplication gamma ideal. Relation between multiplication gamma act and free gamma act was studied. Also, we define the concept of product gamma subacts of gamma act , particularly product gamma subacts of multiplication gamma act then we obtain some related results. Using our concept to introduce new mathematical system which is called the semigroup associative with multiplication gamma act and its basic properties are discussed.
Moreover , we introduce the definitions of pure and idempotent gamma subacts of multiplication gamma acts and clarified their properties . Also, we study the relation between them and a multiplication gamma act . The concept of prime gamma subact is introduce .Some results of this concept are considered . Using this concept to introduce the definition of spectrum gamma acts and investigate it's properties. Finally , we give the notion of topological gamma act and generalize this notion on a some properties of a topological space . The relation between it and(multiplication , cyclic) gamma acts is studied . Also, we introduce another topological space is called the endomorphism topology and we will prove that topological gamma act and a subspace of our topology are homeomorphic.
Summary:
e4d7d4c89f.pdf
