Q(xy) = Q(x)Q(y).
Q(xy) = Q(x)Q(y).

Numbers and Sets - Sebastian Pancratz
Numbers and Sets - Sebastian Pancratz

... Solving linear equations in integers . . . . . . . . . . . . . . . . . . . . . ...
Singularity surfaces
Singularity surfaces

Determine whether each trinomial is a perfect square trinomial. Write
Determine whether each trinomial is a perfect square trinomial. Write

Universiteit Leiden Super-multiplicativity of ideal norms in number
Universiteit Leiden Super-multiplicativity of ideal norms in number

Ring Theory Solutions
Ring Theory Solutions

Acta Acad. Paed. Agriensis, Sectio Mathematicae 27 (2000) 25–38
Acta Acad. Paed. Agriensis, Sectio Mathematicae 27 (2000) 25–38

A SHORT PROOF OF ZELMANOV`S THEOREM ON LIE ALGEBRAS
A SHORT PROOF OF ZELMANOV`S THEOREM ON LIE ALGEBRAS

Lecture Notes for Math 614, Fall, 2015
Lecture Notes for Math 614, Fall, 2015

Quotient Rings of Noncommutative Rings in the First Half of the 20th
Quotient Rings of Noncommutative Rings in the First Half of the 20th

10-2 combine like terms
10-2 combine like terms

... 2-9 Combining Like Terms Additional Example 2C: Combining Like Terms Combine like terms. C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 3a2 + 5b + 11b2 – 4b + 2a2 – 6 (3a2 + 2a2) + (5b – 4b) + 11b2 – 6 5a2 + b + 11b2 – 6 ...
RINGS OF INTEGER-VALUED CONTINUOUS FUNCTIONS
RINGS OF INTEGER-VALUED CONTINUOUS FUNCTIONS

WHICH ARE THE SIMPLEST ALGEBRAIC VARIETIES? Contents 1
WHICH ARE THE SIMPLEST ALGEBRAIC VARIETIES? Contents 1

Triangularizability of Polynomially Compact Operators
Triangularizability of Polynomially Compact Operators

12 The Maximal Ring of Quotients.
12 The Maximal Ring of Quotients.

On the classification of 3-dimensional non
On the classification of 3-dimensional non

FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 27
FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 27

... higher than n). We will discover the moral that the Euler characteristic is better-behaved than h0 , and so we should now suspect (and later prove) that this polynomial is in fact the Euler characteristic, and the reason that it agrees with h0 for m ≥ 0 because all the other cohomology groups should ...
9 The resultant and a modular gcd algorithm in Z[x]
9 The resultant and a modular gcd algorithm in Z[x]

The Z-densities of the Fibonacci sequence
The Z-densities of the Fibonacci sequence

... if the order of α is n then F2n ≡ 0 (mod p) and L2n ≡ 1 (mod p). Thereby we can recover the divisibility properties of the Fibonacci sequence by considering the order α in G(Fp ). Hence we can relate Z(p) to the order of α = (3/2, 1/2) in G(Fp ), as is shown in Theorem 3.5. We define a n-th preimag ...
Notes on Algebraic Structures - Queen Mary University of London
Notes on Algebraic Structures - Queen Mary University of London

Notes on Algebraic Structures
Notes on Algebraic Structures

a(x)
a(x)

1-6
1-6

... Problem of the Day Complete the pyramid by filling in the missing numbers. Each number is the sum of the numbers in the two boxes below it. ...
HEIGHTS OF VARIETIES IN MULTIPROJECTIVE SPACES AND
HEIGHTS OF VARIETIES IN MULTIPROJECTIVE SPACES AND

Exercise help set 4/2011 Number Theory 1. a) no square of an
Exercise help set 4/2011 Number Theory 1. a) no square of an

Eisenstein's criterion

In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers—that is, for it to be unfactorable into the product of non-constant polynomials with rational coefficients.This criterion is not applicable to all polynomials with integer coefficients that are irreducible over the rational numbers, but it does allow in certain important cases to prove irreducibility with very little effort. It may apply either directly or after transformation of the original polynomial.This criterion is named after Gotthold Eisenstein. In the early 20th century, it was also known as the Schönemann–Eisenstein theorem because Theodor Schönemann was the first to publish it.