The Pontryagin Dual group of Q_p
In this post we show that the Pontryagin dual group of $\mathbb{Q}_p$ is isomorphic to itself.
The Pontryagin Dual group of Q_p
The Haar Measure on the Field of p-Adic Numbers
In this post we study the canonical Haar measure on $Q_p$, and give a explicit definition just as the Lebesgue measure.
The Haar Measure on the Field of p-Adic Numbers
Every Regular Local Ring is Cohen-Macaulay
In this post we show that the class of regular local rings (the abstract version of power series rings) is a subclass of Cohen-Macaulay ring.
Every Regular Local Ring is Cohen-Macaulay
The abc Theorem of Polynomials
In this post we show the Mason-Stothers theorem, the so-called $abc$ theorem for polynomials, and derive Fermat's Last theorem and Davenport's inequality for polynomials. These three theorems correspond to the $abc$ conjecture, Fermat's Last Theorem and Hall's conjecture in number theory.
The abc Theorem of Polynomials