紧致性定理在近世代数中的应用

Application of Compactness Theorem in Linear Algebra

模型论中紧致性定理在代数中有很广泛的应用。用紧致性定理证明了若L中的理论.T有任意大特征的整环或除环模型,则T有特征为O的整环或除环模型;若一个语句(?)在任意一个特征为零的整环或除环中为真,则对任意的自然数n,存在素数P>n,使(?)在特征为P的整环或除环中真。

Compactness theorem of model theory in algebra is widely used in the article,the compact theorem proves that if the theory T of L has any major feature of the model of the entire ring or a division ring,then T has 0 characteristics of the entire ring or a division ring model;if a statementφis a feature of zero in any part or the whole ring in addition to true,then for any natural number n,there are prime p > n,so thatφis true in the characteristics p of the entire ring or in addition to ring.