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Michael Morrow
  • Member for 2 years, 6 months
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5 votes

Best self study books for Algebraic Number Theory?

5 votes
Accepted

Is ring $\mathbb{Z}_5[x]/I$ is a field, when: $I=(3x^3+2x+1)\mathbb{Z}_5[x]$?

4 votes

Are Imaginary Numbers as $Real$ as Real Numbers?

4 votes
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Inverse is not connected

3 votes
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How beneficial are Gröbner bases for solving systems of equations

3 votes

Polynomial ring is not a UFD

2 votes
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Function notation to relate Domain and Range

2 votes

Prove that whenever $n$ and $m$ are natural numbers such that $m > n$, then we have $a_{m} > a_{n}$

2 votes
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Showing that a set is closed if $Y$ is Hausdorff

2 votes
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Let $q(x)=1+x+x^2+...+x^n$. Prove that if $p_1(x),..,p_n(x)$ is any basis for $W$, then $p_1(x),...,p_n(x),q(x)$ is a basis for $P_n(\mathbb{R})$

2 votes
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Is the set $\{0,1,2,3,4,5\}$, with the binary operation of "addition, then modulo $3$", a group?

2 votes

What's the maximum and minimum of $\sin Z$ and $\cos Z$ where $Z$ is a complex number?

2 votes
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Better way to write the sum of multiple terms with cross-correlation

2 votes
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Suppose $G$ and $G'$ are grobner bases for the ideal $I$. Show that $\overline{f}^{G} = \overline{f}^{G'}$ for $f \in k[x_1, \cdots, x_n]$

2 votes
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Definition of a Graded Algebra and $R_0$

1 vote

Monomial order refines the partial order of divisibility

1 vote
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Basic question about S-polynomial example

1 vote
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Proof check: Show that, for $n \geq 0$, $n\mathbb{Z} = \{nk : k \in \mathbb{Z} \}$ is not a subgroup of $\mathbb{Z}$ under multiplication.

1 vote
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Proving that the union of compact sets is compact (in $\mathbb{R}$)

1 vote

How can I prove that $\sum _{n=1}^{\infty }\:\:\sin\left(\frac{n}{n^2+1}\right)$ diverges?

1 vote

Decomposition-Group Theory

1 vote
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References for books of Combinatorics

1 vote
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$K$-invariant $F$-homomorphism over finite normal field extension $K/F$

1 vote

Degree of splitting field is either $1$ or $2$

1 vote
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Proving that this homomorphism is onto

1 vote

Unique subfield $L$ of $K=\mathbb{Q}(\sqrt[5]{2},\zeta_5)$ such that $[K:L]=5$

1 vote

Proof Without contradiction $x^2 = 2$ has no rational solutions

1 vote

Proof that units mod $n$ are closed

1 vote
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existence of negative root

0 votes

Equivalent properties of graded ideals