THEOREMS ABOUT LOSS AND CONTINUATION OF UNKNOWNS. SOLVING EXAMPLES OF THEM.

In this article, we . Let I=<f_1,…,f_s>⊂k[x_1,x_2,…,x_n ] -ideal. Then the ideal I_l is called a lost ideal of order l of k[x_(l+1),…,x_n]. I_l=I∩k[x_(l+1),…,x_n ]. In other words, I_l are the results of the system of ideal equations f_1=⋯=f_s=0, where they are polynomials x_1,…,x_l independent of the unknowns. Our task is to show that I_l is an ideal of the polynomial ring k[x_(l+1),…,x_n]. This ideal I=I_0 is called a zero lost ideal. Then, by changing the order, we get another lost ideal.