A hyperfactorial divisibility
نویسنده
چکیده
• Let R be a ring. Let u ∈ N and v ∈ N, and let ai,j be an element of R for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . Then, we denote by (ai,j) 1≤i≤u the u× v matrix A ∈ Ru×v whose entry in row i and column j is ai,j for every (i, j) ∈ {1, 2, ..., u} × {1, 2, ..., v} . • Let R be a commutative ring with unity. Let P ∈ R [X] be a polynomial. Let j ∈ N. Then, we denote by coeffj P the coefficient of the polynomial P before X. (In particular, this implies coeffj P = 0 for every j > degP .) Thus, for every P ∈ R [X] and every d ∈ N satisfying degP ≤ d, we have
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