An Equivalent Proposition of Eisenstein Discrimination Method
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摘要: 判定整系数多项式的不可约性,艾森斯坦因判别法[1](以下简称“艾法1”)是高等代数中给出的主要方法之一。但“艾法1”中所给条件只是一个充分条件,故有些多项式用“艾法1”不能判别其是否可约。本文给出了艾森斯坦因判别法的一个等价命题(以下简称“艾法2”),弥补了“艾法1”的一些不足。Abstract: Eisentein Discrimination Method 1 to decide the irreducibility of the multinomial polynomial of integral coefficients is one of the main methods offered in higher algebra. As the condition given in Eisentein Method 1 is only a sufficient one, whether some multinomial polynomials are irreducible or not can’t be decided by this method. The equivalent proposition given here makes up the weakness of Eisenstein Method 1.
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[1] 北京大学数学力学系几何与代数教研室代数小组.高等代数[M].北京:高等教育出版社,1978.33-34
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