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This is my first post in MSE:

I have completed my Masters in Mathematics.I love to do Abstract Algebra. I have studied Groups,Rings,Fields,Modules and Non-Commutative Rings. But I am weak in Calculus and I don't like doing stuffs like Real Analysis,Complex Analysis.

I want to do PhD in Abstract Algebra as I really want to study it further.

I checked the profiles of different faculty members in different Institutes.None mentioned Abstract Algebra in their profiles.

So I got a bit puzzled.

Can someone please tell me about the topics which are closely related to Abstract Algebra or uses techniques from what I have studied and loved for example Rings,Modules etc as mentioned above.

To make it clear I am no way asking for Research Topics. I only want to find some suitable directions where I can continue studying Abstract Algebra

If this post is not suitable here,please tell me any other suitable site for this.

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    $\begingroup$ Which institutes did you check? Most math departments have at least a few people who do algebra of some sort. $\endgroup$ – Tobias Kildetoft Apr 11 '18 at 17:57
  • $\begingroup$ Check also for algebraic number theory, or algebra and number theory. $\endgroup$ – Dietrich Burde Apr 11 '18 at 18:06
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    $\begingroup$ Algebraic geometry is definitely something you should look into, and perhaps algebraic topology (although based on your comment re: analysis, you might not like that as much - but on the other hand, analysis and topology are very different things). $\endgroup$ – Noah Schweber Apr 11 '18 at 18:08
  • $\begingroup$ @TobiasKildetoft;I checked faculty webpages of various institutes like MIT,Stanford and many others which were high in QS Rankings.But they all said algebraic geometry,representation theory etc. $\endgroup$ – Learnmore Apr 12 '18 at 1:11
  • $\begingroup$ @DietrichBurde; How should I prepare myself if I want to do PhD in Algebra,Number Theory and what are its prerequisites $\endgroup$ – Learnmore Apr 12 '18 at 2:59

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