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6,055 questions
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Do monoid homomorphisms from $X^X$ to a group factor through $\text{Sym}(X)$? [closed]
Let $X$ be a set and let $(X^X,\circ)$ denote the monoid of all maps $f: X\to X$, together with composition. Let $(\text{Sym}(X),\circ)$ be the group of all bijections from $X$ to itself.
Does there ...
- 48.9k
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1
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447
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Integral closure of an ideal [closed]
Let $r^n+a_1r^{n-1}+\cdots+a_n=0$ be an equation of integral dependence of $r$ over an ideal $I$. Does exist a finitely generated ideal $J$, such that $J\subset I$ and $a_i\in J^i$ for all $i=1,\...
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-4
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1
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251
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What are the properties of 3-dimensional split-complex numbers?
I have often encountered claims that 3-dimensional numbers are impossible. But
it seems to me that $\mathbb{R}^3$ with Hadamard multiplication should in fact behave quite similar to split-complex ...
- 10.1k
-6
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2
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1k
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Can I define the polynomial ring A[x] with an isomorphism f: A ---> A[x]? [closed]
I'm sorry if this isn't an appropriate question for MO. I've been reading here for a while, but I still haven't got a good grasp of what's a good question.Given a field A and the polynomial ring A[x], ...
-8
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1
answer
351
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Are there overwhelmingly more finite monoids than finite spaces? [closed]
A function $f:\mathbb{Z}_{\geq 1}\to\mathbb{Z}_{\geq 1}$ overwhelms $g:\mathbb{Z}_{\geq 1}\to\mathbb{Z}_{\geq 1}$ if for any $k\in \mathbb{Z}_{\geq 1}$ the inequality $f(n)\leq g(n+k)$ holds only for ...
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