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### 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 ring relations as generators of a left ideal.

(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 ring relations as generators of a right ideal.

(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 homalg ring.

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

#### 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.

#### 6.5 Ring Relations: Operations and Functions

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