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May
5
asked Question on Frobenius Reciprocity
May
5
comment Proving that the tensor product is generated by $a\otimes b$
@Magdiragdag yes sorry that is what I meant, the stuff generated by the tensors $a\otimes b$. I think there is a problem with this approach though. Say we let $K$ be the module generated by stuff of the form $a\otimes b$. Then take $x,y\in A\otimes B-K$. Then I see no reason as to why we couldn't have $x+y\in K$ and $x+y\neq 0$ which would be a problem for the map.
Apr
30
accepted Proving The Diamond Lemma
Apr
30
comment $\mathbb{C}\otimes_\mathbb{C} \mathbb{C} \cong \mathbb{R}\otimes _\mathbb{R} \mathbb{C}$
Is there a slight subtly here in that we can write a map $f:\mathbb{C}\otimes \mathbb{C}\rightarrow \mathbb{C}$ such $f(a\otimes b)=ab$ and then show that this map is injectvive/surjective. However do we also need to check that this map is well defined, which is a problem as we don't know what $a\otimes b$ is and so we have to define $g:\mathbb{C}\times \mathbb{C}\rightarrow \mathbb{C}$ such that $g(a,b)=a\otimes b$ and then use the universal property to show that the map from before actually exists and is well defined?
Apr
30
accepted Example of a functor on products
Apr
30
accepted Proving that $V(R^*)=V(R)-1$
Apr
30
comment Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple
@JackSchmidt Are you saying that $\{0,g\}$ is an ideal? I am now confused, don't we have $\{0,g\}g=\{0,e\}$ hence this is not an ideal?
Apr
30
accepted Proving that the tensor product is generated by $a\otimes b$
Apr
30
asked Proving that the tensor product is generated by $a\otimes b$
Apr
29
comment Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple
Thanks! Sorry for the pretty trivial question
Apr
29
accepted Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple
Apr
29
comment Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple
So $\{0,e\}$ is not an ideal as $\{0,e\}g\not\subset \{0,e\}$ but $\{0,g\}$ is an ideal right as is $\{0,e+g\}$ so does this choice work?
Apr
29
comment Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple
oh yeah, oops. Yeah if I just leave the last summand off I think I am ok right?
Apr
29
comment $\mathbb{C}\otimes_\mathbb{C} \mathbb{C} \cong \mathbb{R}\otimes _\mathbb{R} \mathbb{C}$
@FabioLucchini Yeah but I am just considering these as abelian groups so this is irrelevant right?
Apr
29
asked Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple
Apr
29
asked $\mathbb{C}\otimes_\mathbb{C} \mathbb{C} \cong \mathbb{R}\otimes _\mathbb{R} \mathbb{C}$
Apr
27
comment Example of a functor on products
@Niels.Remb05 why? they are not products of the same objects?
Apr
27
asked Example of a functor on products
Apr
24
awarded  Popular Question
Apr
23
awarded  Popular Question