Displaying similar documents to “Implicative hyper K -algebras”

Hyper BCI-algebras

Xiao Long Xin (2006)

Discussiones Mathematicae - General Algebra and Applications

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We introduce the concept of a hyper BCI-algebra which is a generalization of a BCI-algebra, and investigate some related properties. Moreover we introduce a hyper BCI-ideal, weak hyper BCI-ideal, strong hyper BCI-ideal and reflexive hyper BCI-ideal in hyper BCI-algebras, and give some relations among these hyper BCI-ideals. Finally we discuss the relations between hyper BCI-algebras and hyper groups, and between hyper BCI-algebras and hyper H v -groups.

Positive Implicative Soju Ideals in BCK-Algebras

Xiao Long Xin, Rajab Ali Borzooei, Young Bae Jun (2019)

Bulletin of the Section of Logic

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The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.

Ultra L I -Ideals in lattice implication algebras and M T L -algebras

Xiaohong Zhang, Ke Yun Qin, Wiesław Aleksander Dudek (2007)

Czechoslovak Mathematical Journal

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A mistake concerning the ultra L I -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an L I -ideal to be an ultra L I -ideal are given. Moreover, the notion of an L I -ideal is extended to M T L -algebras, the notions of a (prime, ultra, obstinate, Boolean) L I -ideal and an I L I -ideal of an M T L -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in M T L -algebra: (1) prime proper L I -ideal and Boolean...

On hyper BCC-algebras.

Borzooei, R.A., Dudek, W.A., Koohestani, N. (2006)

International Journal of Mathematics and Mathematical Sciences

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