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6 Ring Relations
6.1 Ring Relations: Categories and Representations
6.1-1 IsHomalgRingRelations
6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal
6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal
6.1-4 IsRingRelationsRep
6.2 Ring Relations: Constructors
6.3 Ring Relations: Properties
6.3-1 CanBeUsedToDecideZero
6.3-2 IsInjectivePresentation
6.4 Ring Relations: Attributes
6.5 Ring Relations: Operations and Functions

### 6 Ring Relations

#### 6.1 Ring Relations: Categories and Representations

##### 6.1-1 IsHomalgRingRelations

`> IsHomalgRingRelations`( rel ) | ( category )

Returns: `true` or `false`

The GAP category of homalg ring relations.

##### 6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal

`> IsHomalgRingRelationsAsGeneratorsOfLeftIdeal`( rel ) | ( category )

Returns: `true` or `false`

The GAP category of homalg relations of a left module.

(It is a subcategory of the GAP category `IsHomalgRingRelations`.)

##### 6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal

`> IsHomalgRingRelationsAsGeneratorsOfRightIdeal`( rel ) | ( category )

Returns: `true` or `false`

The GAP category of homalg relations of a right module.

(It is a subcategory of the GAP category `IsHomalgRingRelations`.)

##### 6.1-4 IsRingRelationsRep

`> IsRingRelationsRep`( rel ) | ( representation )

Returns: `true` or `false`

The GAP representation of a finite set of relations of a finitely presented homalg module.

(It is a representation of the GAP category `IsHomalgRingRelations` (6.1-1))

#### 6.2 Ring Relations: Constructors

#### 6.3 Ring Relations: Properties

##### 6.3-1 CanBeUsedToDecideZero

`> CanBeUsedToDecideZero`( rel ) | ( property )

Returns: `true` or `false`

Check if the homalg set of relations rel can be used for normal form reductions.
(no method installed)

##### 6.3-2 IsInjectivePresentation

`> IsInjectivePresentation`( rel ) | ( property )

Returns: `true` or `false`

Check if the homalg set of relations rel has zero syzygies.

#### 6.4 Ring Relations: Attributes

#### 6.5 Ring Relations: Operations and Functions

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