Hilbert Basis Theorem 1 Jonathan Backer University of Alberta Edmonton Piotr Rudnicki University of Alberta Edmonton
نویسندگان
چکیده
One can prove the following propositions: (1) Let A, B be finite sequences and f be a function. Suppose rngA∪rngB ⊆ dom f. Then there exist finite sequences f1, f2 such that f1 = f · A and f2 = f · B and f · (A a B) = f1 a f2. (2) For every bag b of 0 holds decomp b = 〈〈∅, ∅〉〉. (3) For all natural numbers i, j and for every bag b of j such that i ¬ j holds b↾i is an element of Bags i. (4) Let i, j be sets, b1, b2 be bags of j, and b ′ 1 , b 2 be bags of i. If b 1 = b1↾i and b 2 = b2↾i and b1 divides b2, then b ′ 1 divides b 2 .
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