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Declare arithmetic with formal variables

I want to create variables in SAGE and and declare arithmetic relations between them. For example, it is easy enough to declare that x1, ..., xn and y1, ..., yn be variables. Is there a way to state that

xi*xj = 0 (in the ring of polynomials, if necessary)

or that

x1 < y1 < x2 < y2 < ...?