hmIII

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20 Questions

views newest activity votes

3

11

votes

2

answers

239

views

Why is it that $\det(\phi-x\text{id})=\sum_{i=0}^n (-1)^ic_ix^i$?

commutative-algebra multilinear-algebra exterior-algebra

mar 28 '12 at 23:50 Georges Elencwajg 45k

4

6

votes

2

answers

183

views

Why does $(2/p)=\prod_{k=1}^{(p-1)/2}2\cos\left(\frac{2\pi k}{p}\right)$?

number-theory

jan 9 at 6:25 lab bhattacharjee 29.2k

3

6

votes

1

answer

149

views

Why is the kernel of this strange polynomial homomorphism what it is?

linear-algebra matrices algebraic-geometry

apr 28 '12 at 21:26 Georges Elencwajg 45k

2

5

votes

2

answers

180

views

Is this quotient ring $\mathbb{C}[z_{ij}]/\ker\phi$ integrally closed?

algebraic-geometry commutative-algebra

nov 9 at 19:48 YACP 9,245

1

5

votes

2

answers

281

views

Examples proving why the tensor product does not distribute over direct products?

modules tensor-products

mar 11 '12 at 15:30 Pierre-Yves Gaillard 8,487

1

4

votes

2

answers

97

views

If $A\equiv 1\pmod{3}$, then $4p=A^2+27B^2$ uniquely determines $A$.

number-theory elementary-number-theory reference-request

feb 6 at 5:01 Gerry Myerson 86k

1

4

votes

4

answers

128

views

If $a^m=b^m$ and $a^n=b^n$ for $(m,n)=1$, does $a=b$? [duplicate]

abstract-algebra ring-theory

jun 25 '12 at 20:49 Arturo Magidin 158k

4

votes

1

answer

115

views

Center of Weyl algebra over a field of characterstic $0$?

abstract-algebra reference-request

apr 12 '12 at 23:21 Mariano Suárez-Alvarez♦ 53.4k

4

votes

2

answers

254

views

How to find the nilpotent elements of $\mathbb{Z}/(\prod p_i^{n_i})$?

commutative-algebra ideals

mar 6 '12 at 16:35 Steve 3,516

4

votes

2

answers

117

views

Why is the kernel of $k[x_1,\dots,x_n]\to k$ a maximal ideal?

commutative-algebra ideals

mar 5 '12 at 3:09 hmIII 211

3

votes

1

answer

101

views

Theorem of Kaplansky, $R$ is a division ring if every element but one is (right) quasi-invertible.

reference-request ring-theory rngs

jul 30 at 22:20 rschwieb 21.2k

3

votes

1

answer

97

views

Change of base property for flat modules?

commutative-algebra modules

mar 16 '12 at 8:07 Georges Elencwajg 45k

2

votes

1

answer

62

views

Why is the cyclic decomposition of a primary torsion module not unique?

abstract-algebra modules

feb 23 at 21:51 YACP 9,245

2

votes

1

answer

34

views

Uniqueness up to sign of $L$ and $M$ in $p=\frac{1}{4}(L^2+27M^2)$.

number-theory reference-request

feb 5 at 23:19 Will Jagy 21.6k

2

votes

1

answer

132

views

Existence of irreducible polynomial of arbitrary degree over finite field without use of primitive element theorem?

field-theory galois-theory finite-fields

jan 27 at 18:30 N. S. 28.1k

2

votes

1

answer

91

views

Determining the sign of the Gauss sum under the change of variable $x\mapsto 1+u$.

number-theory polynomials

jan 23 at 17:29 Victor Wang 141

2

votes

1

answer

93

views

Do $T$-invariant subspaces necessarily have a $T$-invariant complement?

linear-algebra

dec 14 at 7:07 Sanchez 4,313

2

votes

1

answer

120

views

Troubling calculation for a wreath product of groups.

abstract-algebra group-theory

jul 8 at 2:01 Arturo Magidin 158k

2

votes

1

answer

56

views

Finding a $\mathbb{C}$-balanced map from $\mathbb{C}^2\to\mathbb{R}^2$?

modules tensor-products

mar 8 '12 at 8:13 Ted 7,579

2

votes

1

answer

187

views

Why does $k[X,Y]/(XY)$ have two minimal primes?

commutative-algebra

mar 6 '12 at 2:16 Bruno 7,144

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