INVARIANTIVE THEORY OF EQUATIONS IN A FINITE FIELD

INVARIANTIVE THEORY OF EQUATIONS IN A FINITE FIELD
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有限域方程的不变论

DOI：
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发表时间：
1953
期刊：
影响因子：
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通讯作者：
L. Carlitz
L. Carlitz
中科院分区：
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文献类型：
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作者：
Finite Field;L. Carlitz

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具有逆的；这里ti，rqjEGF(Q)和4是系数为EGF(Q)的多项式。变换的全体(1.1)形成与QR字母上的对称群同构的群。如果f=f(i，***，tr)是系数为ecgf(Q)且of=g的任意多项式，则f和g是等价的。如果f(2，*，ir)=g(2，*，tr)，则定义两个多项式f和g相等。由此推论，存在QF不同的多项式。通过前面定义的等价关系，它们被分成一定数量的类；一个简单的组合论证表明，类的数量是
possessing an inverse; here ti, rqjEGF(q) and the 4. are polynomials with coefficients EGF(q). The totality of transformations (1.1) form a group isomorphic with the symmetric group on qr letters. If f=f(i, * * * , tr) is an arbitrary polynomial with coefficients ECGF(q) and Of = g, then f and g are equivalent. Two polynomials f and g are defined as equal if f(2,, * *, Ir) =g(2,, * , tr) for all tj. It follows that there are qf distinct polynomials. By means of the previously defined equivalence relation they are separated into a certain number of classes; a simple combinatorial argument shows that the number of classes is