Undergraduate Module Theory Books (including rings, of course)

[Math Amateur]

For those looking for an undergraduate introduction to module theory there is not a great deal of choice regarding textbooks, but two possible texts are as follows:

"A First Course in Module Theory" by M.E. Keating of Imperial College, London [Publisher: Imperial College Press, 1998]

and

"Introduction to Ring Theory" by Paul Moritz Cohn, late of University College, London. [Springer Undergraduate Mathematics Series]

Keating's book is genuinely undergraduate and is written extremely clearly … …

Cohn's book is more concise, somewhat more advanced and is more of a challenge to follow … ...

Hope that is helpful information for those interested in the introductory theory of modules and their rings ...Peter***NOTE***

A more difficult challenge is to find good introductory books on Algebraic Geometry … ...

 

[Euge]

For those looking for an undergraduate introduction to module theory there is not a great deal of choice regarding textbooks, but two possible texts are as follows:

"A First Course in Module Theory" by M.E. Keating of Imperial College, London [Publisher: Imperial College Press, 1998]

and

"Introduction to Ring Theory" by Paul Moritz Cohn, late of University College, London. [Springer Undergraduate Mathematics Series]

Keating's book is genuinely undergraduate and is written extremely clearly … …

Cohn's book is more concise, somewhat more advanced and is more of a challenge to follow … ...

Hope that is helpful information for those interested in the introductory theory of modules and their rings ...Peter***NOTE***

A more difficult challenge is to find good introductory books on Algebraic Geometry … ...

For algebraic geometry, I recommend Frances Kirwan's book on complex algebraic curves.

 

[Math Amateur]

For algebraic geometry, I recommend Frances Kirwan's book on complex algebraic curves.

Just a further note on undergraduate treatments of module theory:

There is an excellent 598 page abstract algebra text by Paul E. Bland that introduces abstract algebra to undergraduates with clear explanations and a good number of examples, that has a chapter on modules!

Details are as follows:

"The Basics of Abstract Algebra" by Paul E. Bland [Publisher: W.H. Freeman and Company: New York 2002]

Note that Paul Bland has a graduate level book on rings and modules that readers of his first book can follow with to deepen their knowledge. Details are:

"Rings and Their Modules" by Paul E. Bland [Publisher: De Gruyter 2011]Peter

 

[Math Amateur]

For algebraic geometry, I recommend Frances Kirwan's book on complex algebraic curves.

Thanks Euge ... Based on your recommendation, I intend to buy Frances Kirwan's book ... ...

Peter

 

[Euge]

I think, to tackle Kirwan's book, you should have a solid background in linear algebra, complex variables, and general topology. It's a challenging book in my opinion, but I think you'll learn a great deal from it, Peter!

 

[Math Amateur]

I think, to tackle Kirwan's book, you should have a solid background in linear algebra, complex variables, and general topology. It's a challenging book in my opinion, but I think you'll learn a great deal from it, Peter!

Hi Euge,

What books do you recommend reading in order to gain the necessary background in linear algebra? ... in complex variables ... ? ... in general topology?

I would value your suggestions ...

Peter

 

[Euge]

Hi Euge,

What books do you recommend reading in order to gain the necessary background in linear algebra? ... in complex variables ... ? ... in general topology?

I would value your suggestions ...

Peter

Here are my recommendations.

1. Linear Algebra
a) Sheldon Axler, "Linear Algebra Done Right"
b) Stephen Friedberg, Arnold Insel, and Lawrence Spence, "Linear Algebra"
c) Georgi E. Shilov, "Linear Algebra"

2. Complex Variables
a) Lars Ahlfors, "Complex Analysis"
b) John Conway, "Functions of One Complex Variable I"
c) Einar Hille, "Analytic Function Theory, Volume I"
d) Murray Spiegel et al., "Complex Variables"
e) Theodore Gamelin, "Complex Analysis"

3. General Topology
a) John Hocking and Gail Young, "Topology"
b) James Munkres, "Topology"

 

[mathbalarka]

I actually liked Titchmarsh's Theory of Functions and Spiegel's Complex Variables (which I see Euge already mentioned) in Complex Analysis.

 

[Math Amateur]

I actually liked Titchmarsh's Theory of Functions and Spiegel's Complex Variables (which I see Euge already mentioned) in Complex Analysis.

Just a note to let MHB members know of two further undergraduate books on module theory.

They are as follows:

"Elementary Rings and Modules" by Iain T. Adamson [Publisher: Oliver and Boyd 1972 and also published in USA by Harper and Row 1972]"Module Theory: An Approach to Linear Algebra" by T. S. Blyth [Oxford University Press 1990]Iain Adamson's book is a brief (136 pages) and clearly written book which is genuinely undergraduate. I believe Adamson wrote another more advanced book on the same topic.

T. S Blyth's book is a more substantial size (360 pages) and claims to be a self contained introduction to the theory of modules suitable for undergraduates with a basic knowledge of rings, fields and groups. Looking through the book and its contents, it seems suitable for advanced undergraduates or beginning graduates.

Peter