underlyingRing -- The commutative base ring of a DG algebra or DG module

Usage:

S = underlyingRing A

S = underlyingRing M
Inputs:
- A, an instance of the type DGAlgebra,
- M, an instance of the type DGModule,
Outputs:
- S, a ring, The commutative base ring A.ring or M.ring over which the DG structure is defined.

Description

underlyingRing returns the base ring. This is the ring R in the DG algebra A = R\langle T_1, T_2, \ldots \rangle or the DG module M, and it is the ring over which every matrix returned by polyDifferential or moduleDifferential is built.

i1 : R = QQ[x, y] / ideal(x^2, y^2)

o1 = R

o1 : QuotientRing

i2 : A = koszulComplexDGA R

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

o2 : DGAlgebra

i3 : assert(underlyingRing A === R)

i4 : M = koszulComplexDGM R^1

o4 = {Base ring => R                    }
      DG algebra => R[T   ..T   ]
                       1,1   1,2
                                       1
      Natural module => (R[T   ..T   ])
                            1,1   1,2
      Generator degrees => {{0, 0}}
      Differentials on gens => {0}

o4 : DGModule

i5 : assert(underlyingRing M === R)

Ways to use underlyingRing:

underlyingRing(DGAlgebra)
underlyingRing(DGModule)

For the programmer

The object underlyingRing is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:7291:0.

underlyingRing -- The commutative base ring of a DG algebra or DG module

Description

See also

Ways to use underlyingRing:

For the programmer