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Results tagged with ra.rings-and-algebras
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user 169474
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
0
votes
Isomorphism between subgroups by preserving index
Partial answer and remark
I assume that $[A:C] = [B:D] = 2$, since this may not follow from the isomorphisms $C \simeq A/\{-1,1\}$, $D \simeq B/\{-1,1\}$.
The morphism $\pi$ is surjective, like the ca …
- 3,808
17
votes
Accepted
Can nonnegative functions $f(x,y,z)$ be written as a product of pairwise functions $u(x,y) v...
Let $f(x,y,z)=x^2+y^2+z^2$ for $(x,y,z) \in \mathbb{R}^3$. The only zero of $f$ is $(0,0,0)$.
If we had three functions $u,v,w$ such that $f(x,y,z)=u(x,y)v(y,z)w(z,x)$ for every $(x,y,z) \in \mathbb{R …
- 3,808
-1
votes
Submatrices of matrices in $\mathrm{SL}(4, \mathbb{Z})$ with all eigenvalues equal to $1$
It is not a solution since $A$ is not in $GL_2(\mathbb{Z})$, I will try to correct it later.
Let $a,b,c,d$ be in $\mathbb{Z}$ such that $ad-bc=1$.
Set
$$P = \left(\begin{array}{cc}
aI_2 & bI_2 \\
cI_ …
- 3,808