# isSeminormalMA -- Test whether a simplicial monomial algebra is seminormal.

## Synopsis

• Usage:
isSeminormalMA R
isSeminormalMA B
isSeminormalMA M
• Inputs:
• Outputs:

## Description

Test whether the simplicial monomial algebra K[B] is seminormal.

Note that this condition does not depend on K.

For the definition of seminormal see:

Richard G. Swan: On Seminormality, J. Algebra 67, no. 1 (1980), 210-229.

 i1 : B={{1,0,0},{0,2,0},{0,0,2},{1,0,1},{0,1,1}} o1 = {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}} o1 : List i2 : R=QQ[x_0..x_4,Degrees=>B] o2 = R o2 : PolynomialRing i3 : isSeminormalMA R o3 = true i4 : isNormalMA R o4 = false

 i5 : B={{1,0,0},{0,2,0},{0,0,2},{1,0,1},{0,1,1}} o5 = {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}} o5 : List i6 : M=monomialAlgebra B ZZ o6 = ---[x ..x ] 101 0 4 o6 : MonomialAlgebra generated by {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}} i7 : isSeminormalMA M o7 = true i8 : isNormalMA M o8 = false

## Ways to use isSeminormalMA :

• "isSeminormalMA(List)"
• "isSeminormalMA(MonomialAlgebra)"
• "isSeminormalMA(PolynomialRing)"

## For the programmer

The object isSeminormalMA is .