The main subject of the paper are atoms and ideals of a pseudo-BCI-algebra. Many different characterizations of them are given. Some connections between ideals and subalgebras are presented. Conditions for the set \(At(X)\) of atoms of a pseudo-BCI-algebra \(X\) to be an ideal of \(X\) are established.
The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH-algebras are considered.
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