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Equational spectrum of Hilbert varieties

R. Padmanabhan, Sergiu Rudeanu (2009)

Open Mathematics

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.

Foldness of Commutative Ideals in BCK-algebras

Celestin Lele, Salissou Moutari (2006)

Discussiones Mathematicae - General Algebra and Applications

This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.

Fuzzy ideals in BE-algebras.

Song, Seok Zun, Jun, Young Bae, Lee, Kyoung Ja (2010)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Hyper BCI-algebras

Xiao Long Xin (2006)

Discussiones Mathematicae - General Algebra and Applications

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.

Implicative hyper K -algebras

Mohammad Mehdi Zahedi, A. Borumand Saeid, R. A. Borzooei (2005)

Czechoslovak Mathematical Journal

In this note we first define the notions of (weak, strong) implicative hyper K -algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper K -ideals. Also we obtain some relations between these notions and (weak) implicative hyper K -ideals. Finally, we study the implicative hyper K -algebras of order 3, in particular we obtain a relationship between the positive implicative...

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