自由ZYE_3代数

Free ZYE_3 Algebra

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.