Endomorphism Rings - Bland Example 7 - page 10

[Math Amateur]

I am reading Paul E. Bland's book, "Rings and Their Modules".

In Chapter 1: Basic Properties of Rings and Modules, Bland gives endomorphism rings as a basic example of a ring.

The example (Example 7) reads as follows:https://www.physicsforums.com/attachments/3572

I do not feel that I fully understand Bland's notation in this example.

Bland talks about the ring \(\displaystyle \text{End}_{\mathbb{Z} } (G)\) where G is an abelian group ... ... BUT ... ... why do we have \(\displaystyle \mathbb{Z}\) as a subscript in this definition? \(\displaystyle \mathbb{Z}\) seems to have no relevance to this definition.

Hope someone can help ...

Peter

 

[Fallen Angel]

Hi Peter,

Usually, the notation \(\displaystyle End_{R}(M)\) denotes the endomorphism of an R-module M.

Any abelian group can be thought on as a \(\displaystyle \Bbb{Z}\) module.