数学季刊 ›› 2018, Vol. 33 ›› Issue (1): 51-60.doi: 10.13371/j.cnki.chin.q.j.m.2018.01.006
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.
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