Tag: fisica
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If R is a local ring then R[[x]] is local.
Recall that if S is a commutative ring with unit, S is local if and only the set of non unit of S is an ideal, i.e, denoting with S* the unit of S, S-S* is an ideal of S. Now, let m be the maximal ideal of R. We prove that R[[x]] – R[[x]]*…
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Every year admits a Friday the 13th
Theorem: Every year admits a Friday the 13th Proof: Note that a year admits a Friday the 13th if there is a month that begins with Sunday. We denote the days of the week with numbers. Specifically, 0 denotes Sunday, 1 Monday, up to 6, a number that denotes Saturday. If k is a natural…
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Equations in algebraically closed fields.
Let K be an algebraically closed field and f∈K[X,Y] non-constant. Let us prove that f has infinitely many zeros in K x K. Let us define the following sets: A={a ∈K : f(a,y) is constant in K[y]}B={b∈K : f(x,b) is constant in K[x] } if one of them is finite we are done. In fact…
Marco Damele 