摘要
引入了BCK-代数的范数与距离的概念,给出了赋范BCK-代数的一些基本性质,证明了赋范BCK-代数的同构(同态)像和原像仍是赋范BCK-代数,研究了BCK-代数与BCK-代数笛卡儿之间的赋范性质关系.并且引入了赋范BCK-代数的点列极限概念,研究了极限的相关性质.讨论了有界赋范BCK-代数的与模糊BCK-代数的关系.
The notions of norm and distance in BCK-algebras are introduced, and some basic properties in normed BCK-algebras are given. It is obtained that the isomor- phic（homomorphic） image and inverse image of a normed BCK-algebra are still normed BCK-algebras. The relations of normed properties between BCK-algebra and Cartesian prod- uct of BCK-algebras are investigated. The limit notion of sequence of points in normed BCK-algebras is introduced, and its related properties are investigated, the relations between bounded normed BCK-algebras and fuzzy BCK-algebras are discussed.
出处
《数学进展》
CSCD
北大核心
2011年第4期492-500,共9页
Advances in Mathematics（China）
基金
Supported by NSFC(No.11071178)
the special item of Key Laboratory of Education Bureau of Sichuan Province(No.2006ZD050)
