Introduction to Tensor Products - some advice please

  • Context: MHB 
  • Thread starter Thread starter Math Amateur
  • Start date Start date
  • Tags Tags
    Introduction Tensor
Click For Summary

Discussion Overview

The discussion revolves around the concept of tensor products of modules, specifically seeking a clearer understanding and simpler definitions. Participants express confusion regarding the material presented in Dummit and Foote and seek alternative resources or foundational knowledge, such as bilinear forms, to aid their comprehension.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in understanding the introduction to tensor products in Dummit and Foote and requests a simple definition and example.
  • Another participant suggests Keith Conrad's notes as a potentially clearer resource for understanding tensor products.
  • There is a suggestion that studying bilinear forms may be necessary for a better grasp of tensor products, although this remains a point of inquiry.
  • Participants share appreciation for the recommended notes and express intent to study them further.

Areas of Agreement / Disagreement

Participants generally agree that Dummit and Foote's explanations are challenging, and there is a shared interest in finding clearer resources. However, the necessity of studying bilinear forms is still a matter of personal consideration and not universally accepted.

Contextual Notes

Participants have not reached a consensus on the best approach to understanding tensor products, and the discussion includes varying levels of familiarity with the topic.

Math Amateur
Gold Member
MHB
Messages
3,920
Reaction score
48
I am (trying to :-) ) reading Dummit and Foote Section 10.4 on Tensor Products of Modules and am finding D&F's introduction to the topic of tensor products quite bewildering! ...

Can anyone give me a simple definition of a tensor product of modules together with an example to give me a basic understanding of the structure of tensor products of modules ... I would really appreciate such help ...

Alternatively, can anyone give me a reference that gives a good basic introduction to tensor products of modules?

... after looking at a number of texts I am getting the impression that maybe I need to go back and study bilinear forms. What do MHB members think ... do I need to do this?

Appreciate some help and advice ...

Peter
 
Physics news on Phys.org
I'm no pro at algebra, but I'm a fan of Keith Conrad and his notes (you can find the ones on tensor products here).

Hopefully this will make the topic of tensor products easier to understand (I, too, didn't like Dummit and Foote's explanations either)! (Smile)
 
Chris L T521 said:
I'm no pro at algebra, but I'm a fan of Keith Conrad and his notes (you can find the ones on tensor products here).

Hopefully this will make the topic of tensor products easier to understand (I, too, didn't like Dummit and Foote's explanations either)! (Smile)
Thanks Chris, appreciate the help ...

Will give the notes a close look ...

Peter
 
Last edited:
Peter said:
Thanks Chris, appreciate the help ...

Will give the notes a close look ...

Peter
Hi Chris,

Just glanced through the material on tensors ...

Wow! Thank you ... looks at first glance like a wonderful resource!

Will let you know how I go after some detailed study and reflection ...

Thanks so much!

Peter
 

Similar threads

Undergrad The tensor product of tensors confusion
  • · Replies 32 ·
2
Replies
32
Views
4K
High School Array Representation Of A General Tensor Question
  • · Replies 2 ·
Replies
2
Views
2K
High School Transformation Rules For A General Tensor M
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Need some clarifications on tensor calculus please
  • · Replies 5 ·
Replies
5
Views
2K
MHB Tensor Products of Modules and Free Abelian Groups based on Cartesian Product
  • · Replies 2 ·
Replies
2
Views
2K
MHB Example on Z-modules .... Dummit & Foote, Page 339 ....
  • · Replies 1 ·
Replies
1
Views
1K
MHB Tensor Product - Knapp, Chapter VI, Section 6
  • · Replies 5 ·
Replies
5
Views
2K
MHB Tensor Products and the Free Z-module - Bland Propostion 2.2.3 .... ....
  • · Replies 3 ·
Replies
3
Views
1K
MHB The Uniqueness of a Tensor Product
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Example on Z-modules .... Dummit & Foote, Page 339 ....
  • · Replies 2 ·
Replies
2
Views
2K