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K[Z+ ⊕ Zn−1 ] ∼ = K[Y, Z1±1 , . . , Zn−1 Each of them is integrally closed in its ﬁeld of fractions QF(K[L]). If S is normal, then one has a splitting S = S0 ⊕ S as discussed above. It induces an isomorphism K[S] = K[S0 ] ⊗ K[S ]. Therefore K[S] is a Laurent polynomial extension of K[S ]. Since Laurent polynomial extensions preserve essentially all ring-theoretic properties, it is in general no restriction to assume that S is positive (if it is normal). Monomial prime ideals. — The prime ideals in K[S] that are generated by monomials can be easily described geometrically.