给出了一类新的试验多项式，可识别多项式代数的非线性自同构。

We can distinguish nonlinear automorphism of polynomials algebra by using the test polynomials.

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交换环上矩阵代数的可解子代数和幂零子代数的自同构分解问题是一类重要的具有理论意义的研究课题。

It is theoretically important to solve the problems of decomposition of automorphisms of solvable subalgebra and nilpotent subalgebra of matrix algebra over commutative rings.

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在这篇论文中，定理“任意两个具有相同有限个原子的可数无穷布尔代数是同构的”的一个证明被给出。

In this paper, a proof of the theorem on "Any two denumerable Boolean algebras with atoms of the same finite number are isomorphic" is given.

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