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Zbl 0724.06010
Aslam, M.; Thaheem, A.B.
A note on p-semisimple BCI-algebras.
(English)
[J] Math. Jap. 36, No.1, 39-45 (1991). ISSN 0025-5513

Let $X\sp*$ be the set of all endomorphisms of a p-semisimple BCI-algebra (X,$\cdot,0)$ and let M and N be nonempty sets such that $M\subset X$, $N\subset X\sp*$. Then $X\sp*$ is a p-semisimple BCI-algebra and $M\sp{\perp}=\{x\sp*\in X\sp*:$ $x\sp*(x)=0$ for all $x\in M\},\sp{\perp}N=\{x\in X:$ $x\sp*(x)=0$ for all $x\sp*\in N\}$ are closed weakly implicative ideals. Moreover, for any homomorphism T: $X\to X$ there corresponds a unique homomorphism $T\sp*: X\sp*\to\sp*$ such that $x\sp*(Tx)=T\sp*x\sp*(x)$. In this case $Ker(T\sp*)=R(T)\sp{\perp}$ and $Ker(T)=\sp{\perp}R(T\sp*)$, where Ker and R denote the kernel and the range of the homomorphism, respectively.
[W.A.Dudek (Wrocław)]
MSC 2000:
*06F35 BCK-algebras, etc.
03G25 Other algebras related to logic

Keywords: closed ideals; endomorphisms; BCI-algebra; weakly implicative ideals

Cited in: Zbl 0888.06014 Zbl 0794.06016

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