自由ZYE_3代数  

Free ZYE_3 Algebra

作　　者：沈百英[1] 方朝臣[2] 郑恒武[2] 

机构地区：[1]华东化工学院计算机系 [2]曲阜师范大学

出　　处：《华东化工学院学报》1991年第2期219-225,共7页

摘　　要：首先引入自由ZYE_3代数的概念,然后证明其存在性与唯一性,最后讨论自由ZYE_3代数的性质。The concept of free ZYE3 algebra was first proposed, and then its existence and uniqueness were proved. Finally some properties of ZYE3 algebra were discussed.The main conclusions of this paper are as follows:Definition Let S be a nonempty set. A free ZYE3 algebra generated by S is such a ZYE3 algebra F with a map f from S into F that for any ZYE3 algebra X and a map g from S into X there exists a unique homomorphism η preserving zero from F into X which satisfies g=ηf.Theorem For any nonempty set S, there exists a unique free ZYE3 algebra generated by S up to isomorphism.Theorem Let X be a ZYE3 algebra generated by a subset S, 0∈S, and let F be a free ZYE3 algebra generated by T. If α:T→S is a surjection, then X is a homomorphic image of F. In particular, any ZYE3 algebra is a homomorphic image of some free ZYE3 algebra.

关 键 词：ZYE3代数 自由代数 保零同态 嵌入映射 同态象 

分 类 号：O151[理学—数学]