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Jun
27
answered If $I$ and $J$ are distinct ideals in ring $R$ and $f:R \to R'$ is a homomorphism then is $f(I) = f(J)$?
Jun
27
comment If $I$ and $J$ are distinct ideals in ring $R$ and $f:R \to R'$ is a homomorphism then is $f(I) = f(J)$?
Are you trying to disprove the claim in the title, or prove the claim in the body of the question that the books states?
Jun
26
answered Every base of a root system arises as indecomposable positive roots of a regular element?
Jun
25
comment Homotopy equivalence of $S^{2} \vee S^1$ to $S^{2} \cup A$ where A is a line segment joining noth and south poles
This is shown in Chapter 1, Section 2, Example 2 of "Two Criteria for Homotopy Equivalence" in Hatcher. (Not sure about numbering since I'm looking at a hardcopy from 1999.) It uses the fact that if $(X,A)$ satisfies the homotopy extension property with $A$ contractible, then $X$ and $X/A$ are homotopy equivalent by the quotient map. This is proven in Prop 0.2. (Again, not sure of current numbering.)
Jun
22
answered Equality on pg. 40 of Humphrey's Lie Algebras, $\kappa(t_\lambda,t_\mu)=\sum_{\alpha\in\Phi}\alpha(t_\lambda)\alpha(t_\mu)$?
Jun
13
revised How to tell if 3 connected points are connected clockwise or counter-clockwise?
edited tags
Jun
5
answered integral domains and units
May
31
awarded  Nice Answer
May
8
awarded  Enlightened
Apr
29
comment Proving a left ideal in a direct sum is also a right ideal.
@Nishant Can you explain how you know $e$ and $f$ are central?
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.