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Apr
17
comment how many proper subgroups are there in a trivial group{e}?
What are the proper subsets of $\{e\}$? Can a (sub)group be empty?
Apr
16
answered Constructing the groupification of a semigroup (Vakil 1.5.G)?
Apr
12
answered Isn't this a non-surjective epimorphism on the category of sets?
Apr
12
comment Isn't this a non-surjective epimorphism on the category of sets?
@MartinSleziak Sure, will do.
Apr
12
comment Isn't this a non-surjective epimorphism on the category of sets?
The right-cancellative property of $f$ has to hold for all morphisms $B\to C$ for all objects $C$.
Apr
11
answered How to show that the union of an infinite sequence of subgroups is a subgroup?
Apr
10
awarded  group-theory
Mar
14
comment On the definition of critical point
@DBS I think Sard says the set of critical values has measure zero, not necessarily the set of critical points.
Mar
13
comment For sets $A$, $B$, and $C$, why is $A\times B\times C$ is not the same as $(A\times B)\times C$.
Well, you could say an isomorphism in the category of sets is just a bijection.
Mar
12
comment .Show that $H$ is abelian
This seems similar to: math.stackexchange.com/questions/702692/…, but there are some additional hypotheses that make the result make sense.
Mar
12
comment Prove $S$ is an interval of $\mathbb{R}$ $\iff$ it has betweenness
Perhaps your definition of interval just any connected subset of $\mathbb{R}$? Because this is basically Theorem 2.47, p. 42 in Rudin's Principles of Mathematical Analysis.
Mar
11
reviewed Approve Extension of prime ideals to polynomial rings
Mar
11
comment Extension of prime ideals to polynomial rings
If $P$ is prime, $R/P$ is a domain, so $(R/P)[X]$ is again a domain. (Think about the degree of a product of nonzero polynomials with coefficients in a domain.)
Mar
8
revised Why is $\deg(f)$ well-defined?
added 13 characters in body
Mar
8
answered Why is $\deg(f)$ well-defined?
Mar
7
comment If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
@user149418 Yeah, I'm supposing the hypothesis $3\nmid |G|$ is implicitly saying $G$ is finite.
Mar
7
answered If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.
Mar
3
answered Number of left cosets of the special linear group in the general linear group
Mar
1
answered Last step in proof of equivalence results in partition
Feb
28
answered Allen hatcher book exercice 9 chapter 1 ,using Borsuk-Ulam's theorem