On m - Primary Irreducible Ideals in F [ x ,

At the beginning of the last century F. S. Macaulay developed an elegant theory (see [4] Part IV) describing homogeneous ideals in polynomial rings. This theory makes the maximal-primary irriducible ideals I ⊂ Fýz1 , . . . , znü correspond to a single homogeneous inverse polynomial θI ∈ Fýz−1 1 , . . . , z−1 n ü. Macaulay’s theory has recently attracted attention in connection with problems arising in invariant theory and algebraic topology (see e.g., the introduction to [7] and the references cited there). In this note we show how given an inverse binary form θ ∈ Fýx−1, y−1ü one may explicitly write down generators of the corresponding maximal-primary irreducible ideal Iÿθþ⊂ Fýx, yü. As a bonus we obtain an elementary proof of the fact that such ideals are always generated by a regular sequence (see e.g., [13]).