Anki Deck Changes

Note 1: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: om)==wk?k1

modified

An integral domain $D$ is a (nontrivial, $0 \neq 1$) commutative ring without c3:

An integral domain $D$ is a (nontrivial, $0 \neq 1$) commutative ring without c3:

An integral domain $D$ is a (nontrivial, $0 \neq 1$) commutative ring without zerodivisors ($ab = 0 \implies a = 0 \lor b = 0$)

An integral domain $D$ is a (nontrivial, $0 \neq 1$) commutative ring without zerodivisors ($ab = 0 \implies a = 0 \lor b = 0$)

Field-by-field Comparison

Field	Before	After
Text	<p>An {{c1::integral domain $D$}} is a {{c2::(nontrivial, $0 \neq 1$) commutative ring without c3::zerodivisors ($ab = 0 \implies a = 0 \lor b = 0$)}}:</p>	<p>An {{c1::integral domain $D$}} is a {{c2::(nontrivial, $0 \neq 1$) commutative ring}} without {{c3::zerodivisors ($ab = 0 \implies a = 0 \lor b = 0$)}}</p>

Tags: ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields::4._Zerodivisors_and_Integral_Domains

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: sxW-Trt$`+

deleted

$\mathbb{Z}_m^*$ is defined as?

$\mathbb{Z}_m^*$ is defined as?

\[ \overset{\text{def}}{=} \ \{a \in \mathbb{Z}_m \ | \ \gcd(a, m) = 1\} \]

This is the set of all elements in $\mathbb{Z}_m$ that are coprime to $m$.

Note has been deleted

Field-by-field Comparison

Field	Before	After
Text	~~<p>$\mathbb{Z}_m^*$ is defined as?</p>~~
Extra	~~<p>\[ \overset{\text{def}}{=} \ \{a \in \mathbb{Z}_m \ \| \ \gcd(a, m) = 1\} \]</p> <p>This is the set of all elements in $\mathbb{Z}_m$ that are coprime to $m$.</p>~~

Tags: ETH::1._Semester::DiskMat::5._Algebra::3._The_Structure_of_Groups::8._The_Group_Zₘ*_and_Euler's_Function

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: G&Y|dtr7^k

deleted

If the prime factorization of $m$ is $m = \prod_{i=1}^r p_i^{e_i}$ then $\varphi(m)$ is?

If the prime factorization of $m$ is $m = \prod_{i=1}^r p_i^{e_i}$ then $\varphi(m)$ is?

For a prime and :\[\varphi(m) = \prod_{i=1}^r (p_i - 1)p_i^{e_i - 1}\]

Note has been deleted

Field-by-field Comparison

Field	Before	After
Text	~~<p>If the prime factorization of $m$ is $m = \prod_{i=1}^r p_i^{e_i}$ then $\varphi(m)$ is?</p>~~
Extra	~~<p>For a prime and  :\[\varphi(m) = \prod_{i=1}^r (p_i - 1)p_i^{e_i - 1}\]<br></p>~~

Tags: ETH::1._Semester::DiskMat::5._Algebra::3._The_Structure_of_Groups::8._The_Group_Zₘ*_and_Euler's_Function

Field	Before	After
Text	~~<p>\(\mathbb{Z}_m^*\) is defined as?</p>~~
Extra	~~<p>\[ \overset{\text{def}}{=} \ \{a \in \mathbb{Z}_m \ \| \ \gcd(a, m) = 1\} \]</p> <p>This is the set of all elements in \(\mathbb{Z}_m\) that are coprime to \(m\).</p>~~

Field	Before	After
Text	~~<p>If the prime factorization of \(m\) is \(m = \prod_{i=1}^r p_i^{e_i}\) then \(\varphi(m)\) is?</p>~~
Extra	~~<p>For a prime and  :\[\varphi(m) = \prod_{i=1}^r (p_i - 1)p_i^{e_i - 1}\]<br></p>~~