Implicative Pseudo Valuations on Hoops  

作　　者：WANG Mei XIN Xiao-long WANG Jun-tao 

机构地区：[1]School of Mathematics, Northwest University, Xi'an, 710127, P.R. China

出　　处：《Chinese Quarterly Journal of Mathematics》2018年第1期51-60,共10页数学季刊（英文版）

基　　金：Supported by a grant of National Natural Science Foundation of China（11571281）

摘　　要：The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ(x■x') = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic.The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ（x■x＇） = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic.

关 键 词：(implicative) pseudo valuation HOOPS 

分 类 号：O153[理学—数学]