Hoo, C. S.; Jun, Y. B. Essential ideals and homomorphisms in BCI-algebras. (English) Zbl 0779.06013 Math. Jap. 38, No. 3, 597-602 (1993). We consider essential closed ideals of BCI-algebras and show that if \(X\neq \{0\}\) is a BCK-algebra and \(Y\) is a \(p\)-semisimple BCI-algebra, then \(X\) is an essential closed ideal of \((Y-\{0\})\cup X\) where \((Y- \{0\})\cup X\) is the BCI-algebra with \(X\) as its \(p\)-radical and \(Y\) as its \(p\)-semisimple part. It is shown that a closed ideal \(I\) of a BCI- algebra \(X\) is an essential closed ideal if and only if the inclusion map \(I\to X\) is an essential homomorphism. Finally, it is shown that a BCI- algebra has an injective envelope if and only if it is \(p\)-semisimple and its natural abelian group structure has an injective envelope. Reviewer: C.S.Hoo (Edmonton) Cited in 1 Document MSC: 06F35 BCK-algebras, BCI-algebras Keywords:essential closed ideals; BCI-algebras; BCK-algebra; essential homomorphism; injective envelope PDFBibTeX XMLCite \textit{C. S. Hoo} and \textit{Y. B. Jun}, Math. Japon. 38, No. 3, 597--602 (1993; Zbl 0779.06013)