环的反同态满射的性质  

Properties of Anti-Homomorphic Surjection of Rings

作　　者：孙秀娟 王红丽[1] SUN Xiu-juan;WANG Hong-li(School of Mathematics and Calculation Science,Tangshan Normal University,Tangshan 063000,China)

机构地区：[1]唐山师范学院数学与计算科学学院,河北唐山063000

出　　处：《唐山师范学院学报》2022年第3期11-13,共3页Journal of Tangshan Normal University

基　　金：唐山师范学院科学研究基金项目(2022C38),河北省高等教育教学改革与实践项目(2019GJJG542)。

摘　　要：讨论了反同态下两个环的代数结构之间的关系,证明了环R到环R的反同态满射性质:对零元、负元、交换环、单位元的保持性,对子环、理想的保持性和反保持性;若对环R附加一个条件,对整环、主理想、除环、域的保持性;对于加法,a的像的阶是a的阶的因子。In this paper,the properties of anti-homomorphic surjection from ring R to ring R are discussed:the retentions of zero element,negative element,abelian ring and unit element;the retentions and anti-retentions of subring and ideal;the retentions of integral domain,principal ideal,division ring and field(attached a condition to ring R).In addition,the order of the image of a is a factor of the order of a(for addition).

关 键 词：环 子环 反同态满射 环的同态 

分 类 号：O153.3[理学—数学]