An incline has two associative commutative operations and multiplication, with multiplication distributing over addition, idempotent addition and absorption . Neither operation is required here to have an identity. Its natural order is , making addition a join. Multiplication is order-preserving, and products lie below both factors. A finitely generated incline is well-quasi-ordered by its reversed natural order, via the reverse-inclusion well-quasi-ordering of monomial ideals applied to exponent supports.
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