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Sep
7
answered Finding $\lim\limits_{x \to \infty} \sqrt{9x^2+x} - 3x$
Sep
4
awarded  Nice Question
Sep
4
revised What's bad about left $\mathbb{H}$-modules?
added 233 characters in body
Sep
3
comment Quotient objects, their universal property and the isomorphism theorems
Thank you for your answer. What about considering a category with zero morphisms and normal monomorphisms? This would cover at least the category of groups. At any rate I'm still not fully satisfied, as per your comment on your last paragraph... maybe category theory is not the right language to express what is at hand?
Sep
2
revised What's bad about left $\mathbb{H}$-modules?
added 307 characters in body
Sep
2
comment What's bad about left $\mathbb{H}$-modules?
@Soarer: In general, you can define the tensor product of two $R$-modules over a commutative ring, and get a new $R$-module. If your ring is not commutative, then the tensor product does not naturally have the structure of an $R$-module, and thus remains only as an abelian group. If you accept bimodules, you can get a module structure without the ring necessarily being commutative, see en.wikipedia.org/wiki/Tensor_product_of_modules "Additional structure".
Sep
2
revised What's bad about left $\mathbb{H}$-modules?
added 74 characters in body
Sep
2
comment What's bad about left $\mathbb{H}$-modules?
@Soarer: sure, sorry, sometimes I first post a draft of the answer and then repeatedly edit it to add more content.
Sep
2
answered What's bad about left $\mathbb{H}$-modules?
Sep
1
revised Quotient objects, their universal property and the isomorphism theorems
added 2 characters in body; edited tags
Sep
1
comment Quotient objects, their universal property and the isomorphism theorems
@Noah: right. I changed $Top$ to $TVS_k$.
Sep
1
revised Quotient objects, their universal property and the isomorphism theorems
added 9 characters in body
Aug
31
comment Quotient objects, their universal property and the isomorphism theorems
@yoyo: I know what an abelian category is. What does it have to do with this? The category of groups is not abelian, for example, and all that's stated in the question applies to it.
Aug
31
asked Quotient objects, their universal property and the isomorphism theorems
Aug
29
comment How to prove cancellation property of integer multiplication?
Also, what's so fundamental about this lemma?
Aug
22
revised Solutions of homogeneous linear differential equations are a special case of structure theorem for f.g. modules over a PID
edited tags
Aug
21
comment Etymology of $\arccos$, $\arcsin$ & $\arctan$?
@J.M. I've seen them more frequently with the arg- prefix, presumably as an apocope for "argument".
Aug
20
asked Solutions of homogeneous linear differential equations are a special case of structure theorem for f.g. modules over a PID
Aug
20
comment Surprising Generalizations
@Qiaochu: Do you have a reference where I could see the details of this example? Thank you.
Aug
12
accepted Are the axioms for abelian group theory independent?