Split Epimorphisms .... Bland Proposition 3.2.4 ....

  • MHB
  • Thread starter Math Amateur
  • Start date
  • Tags
    Split
In summary, the conversation discusses Proposition 3.2.4 in Paul E. Bland's book "Rings and Their Modules." The speaker is currently focused on Section 3.2 and needs help understanding the proposition. It is explained that the proposition can be established using the remark after definition 3.2.2 and proposition 3.2.3. The speaker, Peter, thanks the other person for their help.
  • #1
Math Amateur
Gold Member
MHB
3,990
48
I am reading Paul E. Bland's book "Rings and Their Modules" ...

Currently I am focused on Section 3.2 Exact Sequences in [FONT=MathJax_Main]Mod[/FONT][FONT=MathJax_Math]R[/FONT] ... ...

I need some help in order to fully understand Proposition 3.2.4 ...

Proposition 3.2.4 reads as follows:
View attachment 8076
Can someone please explain exactly how Proposition 3.2.3 establishes Proposition 3.2.4 ...
Help will be much appreciated ...

Peter
 
Physics news on Phys.org
  • #2
Hi Peter,

This is a consequence of the remark after definition 3.2.2.

In the case of proposition 3.2.4, $g':M_2\to M$ is a split monomorphism with splitting map $g$, and you can use proposition 3.2.3.
 
  • #3
castor28 said:
Hi Peter,

This is a consequence of the remark after definition 3.2.2.

In the case of proposition 3.2.4, $g':M_2\to M$ is a split monomorphism with splitting map $g$, and you can use proposition 3.2.3.
Thanks for the help, castor28 ...

Peter
 

What is a split epimorphism?

A split epimorphism is a type of morphism in category theory. It is a function between two objects where there exists another function that, when composed with the original function, results in the identity function on the codomain of the original function.

What is Proposition 3.2.4 in Bland's work?

Proposition 3.2.4 is a specific proposition in Bland's work, which is a mathematical text discussing category theory. It is a statement that follows from previous propositions and lemmas and contributes to the overall understanding of the topic being discussed.

How is split epimorphism related to other types of morphisms?

Split epimorphism is related to other types of morphisms, such as regular epimorphism and strong epimorphism. Regular epimorphism is a weaker form of split epimorphism, while strong epimorphism is a stronger form. Split epimorphism falls in the middle of these two types of morphisms in terms of strength.

What are some examples of split epimorphisms?

An example of a split epimorphism is the function from the set of real numbers to the set of positive real numbers, where the inverse function is the square root function. Another example is the projection map from a product category to one of its components.

What is the significance of Bland Proposition 3.2.4 in category theory?

Bland Proposition 3.2.4 is significant in category theory because it helps to establish the properties and relationships of different types of morphisms, specifically split epimorphism. It also contributes to the understanding of category theory and its applications in mathematics and other fields.

Similar threads

I Split Epimorphisms .... Bland Proposition 3.2.4 ....
    • Linear and Abstract Algebra
Replies
4
Views
1K
I Split Monomorphisms .... Bland Defn 3.2.2 & Propn 3.2.3 ....
    • Linear and Abstract Algebra
Replies
5
Views
1K
MHB Split Monomorphisma .... Bland Definition 3.2.2 & Proposition 3.2.3 ....
    • Linear and Abstract Algebra
Replies
2
Views
879
MHB Split Short Exact Sequences .... Bland, Proposition 3.2.6 .... .... Another Question ....
    • Linear and Abstract Algebra
Replies
1
Views
942
MHB Direct Sums of Noetherian Modules .... Bland Proposition 4.2.7 .... ....
    • Linear and Abstract Algebra
Replies
2
Views
1K
MHB Irreducible Elements and Maximal Ideals in Integral Domains ....
    • Linear and Abstract Algebra
Replies
16
Views
2K
I Split Short Exact Sequences .... Bland, Proposition 3.2.6 ....
    • Linear and Abstract Algebra
Replies
3
Views
1K
MHB Direct Products of Modules .... Bland Proposition 2.1.4 .... .... Canonical Injections ....
    • Linear and Abstract Algebra
Replies
4
Views
1K
MHB Principal Ideal Rings and GCDs .... .... Bland Proposition 4.3.3
    • Linear and Abstract Algebra
Replies
1
Views
988
MHB Split Short Exact Sequences .... Bland, Proposition 3.2.6 .... ....
    • Linear and Abstract Algebra
Replies
2
Views
942

Hot Threads

Recent Insights

Back
Top