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Pseudo-BCH-algebras

100%

Walendziak A.

nr 1

5-19

The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH-algebras are considered.

On implicative and maximal ideals of BL-algebras

100%

Walendziak A.

nr 2

In the theory of MV-algebras, implicative ideals are studied by Hoo and Sessa. In this paper we define and characterize implicative ideals of BL-algebras. We also investigate maximal ideals of BL-algebras and prove that if an ideal is prime and implicative, then it is maximal. Moreover, we show that an ideal is maximal if and only if the quotient BL-algebra is a simple MV-algebra. Finally, we give the homomorphic properties of implicative and maximal ideals.

On branchwise commutative pseudo-BCH algebras

100%

Walendziak A.

tom 71

nr 2

Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra.

Some characterizations of pseudo-BL-chains

63%

Walendziak A. , Wojciechowska-Rysiawa M.

Commentationes Mathematicae

2011

tom 51

nr 2

Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.