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Tagged with prime-factorization unique-factorization-domains
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Factorization Question
I need help factoring this problem: anything is appreciated. I have attempted this problem but I haven't been able to solve it so...here it is:
$$\frac{a^2 - ab + ab^2}{a^2 - b^2 + ab^2 +b^3}$$
...
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Are there infinitely many real quadratic number fields with unique factorization?
Unique factorization is a commutative ring in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units.
I'm ...
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Does Shor's algorithm work for noncommutitive or nonassociative algebras?
Shor's algorithm is said to solve the hidden subgroup problem for finite Abelian groups, at least according to the Wikipedia article I read. This means that it can be used to solve factoring or ...
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Unique factorization in 3-sphere coordinate ring
For $n\geqslant 1$ define $$A_n=\mathbb{C}[X_0,X_1,\dots,X_n]\Bigg/\left(\sum_{i=0}^{n}X^2_i-1\right).$$
I would like to prove that $A_3$ is a unique factorization domain.
For $A_2$ it is not true ...
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