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i'm trying to solve the following problem: let $k$ be a field, $k=k(x)$ the field of fractions of $k[x]$ and $u \in k$. show that $k= k(u)$ if and only if $u=\frac{ax+b}{cx+d}$ for some $a,b,c,d \in ... polynomials field-theory asked yesterday quentin bronze badges vote answer views existence of infinite...
let $r$ be a ufd, $k$ its field of fractions, $f(x) \in r[x]$, and assume $f(x) = lpha(x)eta(x)$ with $lpha(x), eta(x)$ in $k[x]$. prove that there exists $c \in k^ imes$ such that $c\... abstract-algebra polynomials ring-theory factoring unique-factorization-domains asked dec ' at : al jebr gold badges...
khinchin integral kolmogorov integral lebesgue–stieltjes integral pettis integral pfeffer integral riemann–stieltjes integral regulated integral integration methods by parts substitution inverse functions changing order trigonometric substitution euler substitution weierstrass substitution partial fractions...
brachytherapy offers an excellent non-invasive solution to complement or replace surgery for skin cancer. with our specialized solutions, a high radiation dose can be delivered to the tumor in a few fractions with a low dose to the surrounding area, providing a short and effective treatment. ensuring...
called "ml red boost", which reduces the conditions that inhibit bacteria from executing proper malolactic fermentation. with this, lallemand gave winemakers a natural solution for solving stuck malolactic fermentation in red wines with high polyphenol contents. x first formulated multi-strain yeast fractions...