模型论在环论中的应用  

Model on the Application of Theory in the Ring

作　　者：段彦峰[1] 陈国龙[1] 武成伟[1] 

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2012年第3期32-33,共2页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高校自然科学研究重点项目(2005KJ032ZD)

摘　　要：模型论中紧致性定理在代数中有很广泛的应用.文章用紧致性定理证明了,若L中的理论T有任意大特征的无零因子幺环模型,则T有特征为0的无零因子幺环模型;若一个语句φ在任意一个特征为0的无零因子幺环中为真,则对任意的自然数n,存在素数p>n,使φ在特征为p的无零因子环中真.Compactness theorem of model theory in algebra has a very wide range of applications. Article with the compact theorem proved that if the theory T of L has any large unitary nonzero factor ring model, T has characteristic 0 without zero factor model of unitary ring; if a statement is true in any non-zero factor unitary ring, then for any natural number n, there is a prime number n〉p, so that it is true in the non - zero factor ring of characteristics p.

关 键 词：模型论 紧致性定理 无零因子幺环 

分 类 号：O141.4[理学—数学]