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oppositeRing -- Creates the opposite ring of a noncommutative ring

Description

Given a noncommutative ring A, this creates a noncommutative ring whose defining ideal is generated by the "opposites" - elements whose noncommutative monomial terms have been reversed - of the generators of the defining ideal of A.

i1 : R = QQ[q]/ideal{q^4+q^3+q^2+q+1}

o1 = R

o1 : QuotientRing
 
i2 : A = skewPolynomialRing(R,q,{x,y,z,w})
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

o2 = A

o2 : FreeAlgebraQuotient
 
i3 : x*y == q*y*x

o3 = true
 
i4 : Aop = oppositeRing A
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.

o4 = Aop

o4 : FreeAlgebraQuotient
 
i5 : y*x == q*x*y

o5 = true

See also

Ways to use oppositeRing:

  • oppositeRing(FreeAlgebra)
  • oppositeRing(FreeAlgebraQuotient)

For the programmer

The object oppositeRing is a method function.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/AssociativeAlgebras/doc.m2:1039:0.