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Definition of a Ring Part 1

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In this video we introduce the definition of a mathematical ring.
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Text Comments (15)
Robleh100 (11 days ago)
I would say a ring could never be an infinite set of symbols. Rings are created from a finite set of symbols, for example, the 0-9 symbols in an arithmetic ring. In fact, infinite symbolization would make operation based mathematics impossible.
Robleh100 (5 days ago)
BTW, to be exact, I meant UNIQUE infinite set of symbols. If we require the symbols to always be unique, there is where the whole system would break down. The precisian in me wouldn't let me not correct that comment.
Robleh100 (10 days ago)
Yes, precisely. the integers represent infinite augmentation with a finite set of symbols under the usual group operations. It is something that I've ruminated upon in a website article. If we could create an infinite alphabet (imprecise language here) of primitives, group operations would break down. So, think of having continually changing symbols to represent the integers and a group operation like + would be impossible. It was a minor criticism, all in all, your lectures are quite enjoyable, a little too slow in developing your concepts, but fun nonetheless.
Ben1994 (11 days ago)
The ring of Integers
Shanthi Visalakshi (8 months ago)
your lectures are excellent
Shahe Shaverdi (1 year ago)
I should just be paying the tuition fees for all of my abstract algebra courses straight to you...
Pranav BVN (1 year ago)
In the identity property mentioned under the axioms, should the 0 also be in the ring to satisfy such property? thanks for the help!
Conrad Complexor (2 years ago)
I'll be using this to help me through ring theory while I play catch-up on abstract algebra and group theory. Thanks for making these!
Mahwish M (2 years ago)
Thank you so much for your videos, I really appreciate it! I have missed a lot of lectures on Rings, and so I'm thinking of watching your Ring theory playlist! Like it so far :)
Nilo de Roock (2 years ago)
Which book(s) do you recommend on the subject?
Nik Star (1 month ago)
This is way too late, but for future readers of this comment: Joseph J. Rotman's 'Advanced Modern Algebra' is a nice compilation of theorems. Rings are in chapter A-3.
Lord Coultas (2 years ago)
+Nilo de Roock If you're looking for a graduate level text in Abstract Algebra, my university uses Algebra by Thomas W. Hungerford. It works like a compendium of the subject.
Hugh Jones (2 years ago)
+Nilo de Roock "A Survey of Modern Algebra" is a classic textbook which has stood the test of time. It covers rings, amongst other algebraic topics.
Mahwish M (2 years ago)
+Nilo de Roock I am not sure what is recommended , but at my university we are using Introduction to Algebra 2nd edition by P. J. Cameron and so far it seems good :)

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