Understanding Rings of Invariant Polynomials
Ashley, Dawn E.
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This paper is designed to introduce undergraduates with some knowledge of abstract algebra to the field of invariant theory. After defining representations and invariant polynomials, key theorems such as Noether's bound are introduced and explained. Two examples are calculated fully F2[x 1, x 2] z3 and F2 [x 1, x 2, x 3] z 7 x z 3 . Finally, a minimal generating set for F2 [ x1, x 2, x 3] z 7 is given.