Abstract

The notions of pseudo-atoms, pseudo-$BCI$ ideals and pseudo-$BCI$ homomorphisms in pseudo-$BCI$ algebras are introduced. Characterizations of a pseudo-$BCI$ ideal are displayed, and conditions for a subset to be a pseudo-$BCI$ ideal are given. The concept of a $\diamond$-medial pseudo-$BCI$ algebra is also introduced, and its characterization is provided. We show that every pseudo-$BCI$ homomorphic image and preimage of a pseudo-$BCI$ ideal is also a pseudo-$BCI$ ideal.

Keywords: Pseudo-$BCK/BCI$-algebra, pseudo-atom, pseudo-$BCI$ ideal, pseudo-$BCI$ homomorphism.

MSC: 06F35, 03G25

Pages:  39--46     

Volume  58 ,  Issue  1$-$2 ,  2006