DGIdeal + DGIdeal -- Sum of two DG ideals

Operator: +
Usage:

K = I + J
Inputs:
- I, an instance of the type DGIdeal,
- J, an instance of the type DGIdeal, With I.dgAlgebra === J.dgAlgebra.
Outputs:
- K, an instance of the type DGIdeal, The DGIdeal with K.natural = I.natural + J.natural.

Description

Preserves d-closure because d(I + J) \subset dI + dJ \subset I + J.

i1 : R = ZZ/101[x, y]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA R

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o2 : DGAlgebra

i3 : Anat = A.natural

o3 = Anat

o3 : PolynomialRing, 2 skew commutative variable(s)

i4 : I = dgIdeal(A, {x_Anat})

o4 = DGIdeal of Anat
     generators => | x |

o4 : DGIdeal

i5 : J = dgIdeal(A, {y_Anat})

o5 = DGIdeal of Anat
     generators => | y |

o5 : DGIdeal

i6 : K = I + J

o6 = DGIdeal of Anat
     generators => | y x |

o6 : DGIdeal

i7 : isWellDefined K

o7 = true

i8 : (I + J) == (J + I)

o8 = true

The zero DGIdeal is a two-sided identity for +.

i9 : Z = dgIdeal(A, {})

o9 = DGIdeal of Anat
     generators => 0

o9 : DGIdeal

i10 : (Z + I) == I

o10 = true

Ways to use this method:

DGIdeal + DGIdeal -- Sum of two DG ideals

The source of this document is in DGAlgebras/doc.m2:2470:0.

DGIdeal + DGIdeal -- Sum of two DG ideals

Description

See also

Ways to use this method: