In this post, we continue the discussion from a previous post about the existence of a suitable sine angle product identity.
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Author: Nihal Uppugunduri
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Starting Intro to Abstract Algebra
I’ve started writing a textbook for Intro to Abstract Algebra! You can check it out here (in-progress, published incrementally).
It seems natural to try to generalize the group ring construction to algebraic structures other than groups and rings. We do so here.
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Removing Proper Classes via Universal Sets
Can we avoid ever needing to mention proper classes in math by restricting to subsets of a universal working set?
Let 
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Rings as Modules Over Themselves
In this note, we address some questions I had concerning rings when viewed as modules over themselves.
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Constructing Compatible Operations 2
In this post, we continue the discussion from the previous in the series.
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An Abstract Approach to Generating Sets 4
In this post, we continue our discussion from the previous in the series.
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Constructing Compatible Operations
Recently in my ring theory class I heard about the theorem that if a ring satisfies 
Recently, I have been thinking about the unreasonable effectiveness of definitions in mathematics. Without making any additional assumptions or knowing any additional information about a situation, by simply making judicious definitions and studying their theory, we can get a lot farther than we could without those definitions. (As you might have noticed, “unreasonable” here is a nod to Eugene Wigner’s classic piece.) Upon further thought, it seems somewhat baffling that this works so well, especially in certain cases.
