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If, in the above commutative diagram of modules and module homomorphisms the columns and two upper rows are exact, then so is the bottom row.

The Eisenstein units are the Eisenstein integers +/-1, +/-omega, +/-omega^2, where omega = 1/2(-1+isqrt(3)) (1) omega^2 = 1/2(-1-isqrt(3)). (2)

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

E(a,b)/p denotes the elliptic group modulo p whose elements are 1 and infty together with the pairs of integers (x,y) with 0<=x,y<p satisfying y^2=x^3+ax+b (mod p) (1) with a ...

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

An Euler pseudoprime to the base b is a composite number n which satisfies b^((n-1)/2)=+/-1 (mod n). The first few base-2 Euler pseudoprimes are 341, 561, 1105, 1729, 1905, ...

The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...