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On maximal ideals of pseudo MV-algebras

Dymek G., Walendziak A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

Vol. 47, [Z] 1

117-126

Fuzzy maximal ideals of pseudo MV-algebras

Dymek G.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

Vol. 47, [Z] 1

31-46

The notion of fuzzy maximal ideals of a pseudo MV-algebra is introduced, and its characterizations are established.

Test spaces, pseudo-effect algebras, and tensor product of pseudo-effect algebras

Dvurečenskij A.

Demonstratio Mathematica

2002

Vol. 35, nr 4

699-715

Inspiring the ideas of the test spaces of effect algebras, we introduce test spaces of pseudo-effect algebras. We show that there is a one-to-one correspondence among algebraic test spaces and pseudo-effect algebras. This correspondence gives a test on a pseudo-effect algebra as a decomposition of unity, which corresponds to hypothesis in the statistical models. This correspondence allows us to define a tensor product of pseudo-effect algebras as well as bounded Boolean power. In addition, we introduce PMV-test spaces which forces pseudo MV-algebras.