Anki Deck Changes

Commit: aecd1959 - fix ring no identity

Author: obrhubr <obrhubr@gmail.com>

Date: 2025-12-30T23:17:45+01:00

Changes: 6 note(s) changed (0 added, 6 modified, 0 deleted)

Note 1: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Classic
GUID: EOU=o(/Tm!
modified

Before

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A ring has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A ring has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
Multiplicative group:
  • closure
  • associativity
  • distributivity

After

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A ring has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A ring has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
  • commutative
Multiplicative group:
  • closure
  • associativity
  • identity
  • distributivity
Field-by-field Comparison
Field Before After
Back Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>distributivity</li></ul> Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li><li>commutative</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>identity</li><li>distributivity</li></ul>
Tags: ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields

Note 2: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Classic
GUID: Jyob1i~-v!
modified

Before

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A commutative ring has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A commutative ring has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
Multiplicative group:
  • closure
  • associativity
  • distributivity
  • commutative

After

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A commutative ring has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A commutative ring has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
  • commutative
Multiplicative group:
  • closure
  • associativity
  • identity
  • distributivity
  • commutative
Field-by-field Comparison
Field Before After
Back Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>distributivity</li><li>commutative</li></ul> Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li><li>commutative</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>identity</li><li>distributivity</li><li>commutative</li></ul>
Tags: ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields

Note 3: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: qFYoZgCSMu
modified

Before

Front

ETH::1._Semester::DiskMat::6._Logic::2._Proof_Systems::4._Proof_Systems_in_Theoretical_Computer_Science_*
The predicate \(\tau\) defines the {{c1:: set of strings \(L \subseteq \{0, 1\}\) that correspond to true statements}}.

Back

ETH::1._Semester::DiskMat::6._Logic::2._Proof_Systems::4._Proof_Systems_in_Theoretical_Computer_Science_*
The predicate \(\tau\) defines the {{c1:: set of strings \(L \subseteq \{0, 1\}\) that correspond to true statements}}.

After

Front

ETH::1._Semester::DiskMat::6._Logic::2._Proof_Systems::4._Proof_Systems_in_Theoretical_Computer_Science_*
The predicate \(\tau\) defines the set {{c1::of strings \(L \subseteq \{0, 1\}\) that correspond to true statements}}.

Back

ETH::1._Semester::DiskMat::6._Logic::2._Proof_Systems::4._Proof_Systems_in_Theoretical_Computer_Science_*
The predicate \(\tau\) defines the set {{c1::of strings \(L \subseteq \{0, 1\}\) that correspond to true statements}}.
Field-by-field Comparison
Field Before After
Text The predicate&nbsp;\(\tau\)&nbsp;defines the {{c1:: set of strings&nbsp;\(L \subseteq \{0, 1\}\)&nbsp;that correspond to true statements}}. The predicate&nbsp;\(\tau\)&nbsp;defines the set {{c1::of strings&nbsp;\(L \subseteq \{0, 1\}\)&nbsp;that correspond to true statements}}.
Tags: ETH::1._Semester::DiskMat::6._Logic::2._Proof_Systems::4._Proof_Systems_in_Theoretical_Computer_Science_*

Note 4: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Classic
GUID: uFE6t!4Hr%
modified

Before

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A field has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A field has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
Multiplicative group:
  • closure
  • associativity
  • distributivity
  • identity
  • no zero-divisor
  • inverse

After

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A field has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
A field has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
  • commutative
Multiplicative group:
  • closure
  • associativity
  • distributivity
  • identity
  • no zero-divisor
  • inverse
Field-by-field Comparison
Field Before After
Back Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>distributivity</li><li>identity</li><li>no zero-divisor</li><li>inverse</li></ul> Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li><li>commutative</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>distributivity</li><li>identity</li><li>no zero-divisor</li><li>inverse</li></ul>
Tags: ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields

Note 5: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Classic
GUID: y|z>._M[it
modified

Before

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
An integral domain has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
An integral domain has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
Multiplicative group:
  • closure
  • associativity
  • distributivity
  • identity
  • no zero-divisors

After

Front

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
An integral domain has the following properties:

Back

ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields
An integral domain has the following properties:
Additive Group:
  • closure
  • associativity
  • identity
  • inverse
  • commutative
Multiplicative group:
  • closure
  • associativity
  • distributivity
  • identity
  • no zero-divisors
Field-by-field Comparison
Field Before After
Back Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>distributivity</li><li>identity</li><li>no zero-divisors</li></ul> Additive Group:<br><ul><li>closure</li><li>associativity</li><li>identity</li><li>inverse</li><li>commutative</li></ul><div>Multiplicative group:</div><div></div><ul><li>closure</li><li>associativity</li><li>distributivity</li><li>identity</li><li>no zero-divisors</li></ul>
Tags: ETH::1._Semester::DiskMat::5._Algebra::5._Rings_and_Fields

Note 6: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: w49b;wY}uY
modified

Before

Front

ETH::1._Semester::LinAlg::2._Matrices::1._Matrices_and_linear_combinations::1._Matrix-Vector_multiplication
The {{c2::rank of a matrix \(\textbf{rank}(A), A \in \mathbb{R}^{m \times n}\) is a number between 0 and n}} which .

Back

ETH::1._Semester::LinAlg::2._Matrices::1._Matrices_and_linear_combinations::1._Matrix-Vector_multiplication
The {{c2::rank of a matrix \(\textbf{rank}(A), A \in \mathbb{R}^{m \times n}\) is a number between 0 and n}} which .
A column is independent if it is not the linear combination of the previous ones (or the next ones, if you do it the other way round).

After

Front

ETH::1._Semester::LinAlg::2._Matrices::1._Matrices_and_linear_combinations::1._Matrix-Vector_multiplication
The {{c2::rank of a matrix \(\textbf{rank}(A), A \in \mathbb{R}^{m \times n}\) is a number between 0 and n}} which counts the number of independent columns.

Back

ETH::1._Semester::LinAlg::2._Matrices::1._Matrices_and_linear_combinations::1._Matrix-Vector_multiplication
The {{c2::rank of a matrix \(\textbf{rank}(A), A \in \mathbb{R}^{m \times n}\) is a number between 0 and n}} which counts the number of independent columns.
A column is independent if it is not the linear combination of the previous ones (or the next ones, if you do it the other way round).
Field-by-field Comparison
Field Before After
Text The {{c2::rank of a matrix \(\textbf{rank}(A), A \in \mathbb{R}^{m \times n}\)&nbsp;is a number between 0 and n}} which {{c1:counts the number of independent columns}}. The {{c2::rank of a matrix \(\textbf{rank}(A), A \in \mathbb{R}^{m \times n}\)&nbsp;is a number between 0 and n}} which {{c1::counts the number of independent columns}}.
Tags: ETH::1._Semester::LinAlg::2._Matrices::1._Matrices_and_linear_combinations::1._Matrix-Vector_multiplication
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