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On BG-algebras

Kim C., Kim H.

Demonstratio Mathematica

2008

Vol. 41, nr 3

497-505

In this paper we introduce the notion of BG-algebras which is a generalization of BG-algebras. We construct a BG-algebra from a non-empty set, which is non-group-derived. Moreover, using the notion of normal subalgebra, we obtain several isomorphism theorems of BG-algebra and related properties.

When is a BCC-algebra equivalent to an MV-algebra?

Chajda I., Halas R., Kuhr J.

Demonstratio Mathematica

2007

Vol. 40, nr 4

759-768

The aim of this paper is to characterize BCC-algebras which are term equivalent to MV-algebras. It turns out that they arę just the bounded commutative BCC-algebras. Purther, we characterize congruence kernels as deductive systems. The explicit description of a principal deductive system enables us to prove that every subdirectly irreducible bounded commutatwe BCC-algebra is a chain (with respect to the induced order) .

Łukasiewicz residuation algebras with infimum

Figallo A. V., Figallo A., Figallo M., Ziliani A.

Demonstratio Mathematica

2007

Vol. 40, nr 4

751-758

Łukasiewicz residuation algebras with an underlying ordered structure of meet semilattice (or iŁR-algebras) are studied. These algebras are the algebraic counter-part of the {->, lambda}-fragment of Łukasiewicz's many-valued logie. An equational basis for this class of algebras is shown. In addition, the subvariety of (n + 1)-valued iŁR-algebras for O < n < u is considered. In particular, the structure of the free finitely generated (n + 1)-valued iŁR-algebra is described. Moreover, a formuła to compute its cardinal number in terrns of n and the number of free generators is obtained.

Some examples of involutory BCK-algebras

Huang Y.

Demonstratio Mathematica

2005

Vol. 38, nr 4

793--798

K. Iseki raised some unsolved problems on BCK-algebras in 1979. One of them is as follows: Is there a non-commutative BCK-algebra satisfying NNx = x? By giving some examples of such algebras, A. Grzaslewicz definitely answered this problem in 1980. Based on Grzaslewicz's work, we give some further examples in this paper.