Let I=(f1,…,fn) and J=(g1,…,gm) be two ideals generated by regular sequences of monomials in the polynomial ring R=k[x1,x2,…,xu]

Show that

where p(IJ) is the polarization of IJ, ΔI is the simplicial complex corresponding to the squarefree monomial ideal I, and ΔJ is the simplicial complex corresponding to the squarefree monomial ideal I.

The cerebrum makes complex learning and abstract thinking possible and is the largest part of the brain.

"Love" is an example of abstract language as it represents a complex concept or emotion that is not easily defined or tangible.

The word problem is an abstract noun.

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