2,340 research outputs found

    Kite Pseudo Effect Algebras

    Full text link
    We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least non-trivial normal ideal

    Pseudo MV-algebras and Lexicographic Product

    Full text link
    We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital â„“\ell-group and an â„“\ell-group that is not necessary Abelian. We introduce (H,u)(H,u)-perfect pseudo MV-algebras and strong (H,u)(H,u)-perfect pseudo MV-algebras, the latter ones will have a representation by a lexicographic product. Fixing a unital â„“\ell-group (H,u)(H,u), the category of strong (H,u)(H,u)-perfect pseudo MV-algebras is categorically equivalent to the category of â„“\ell-groups.Comment: arXiv admin note: text overlap with arXiv:1304.074

    On a New Construction of Pseudo BL-Algebras

    Full text link
    We present a new construction of a class pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop AA. Using two injective mappings from one set, JJ, into the second one, II, and with an identical copy A‾\overline A with the reverse order we construct a pseudo BL-algebra where the lower part is of the form (A‾)J(\overline A)^J and the upper one is AIA^I. Starting with a basic commutative hoop we can obtain even a non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with non-commuting negations. We describe the construction, subdirect irreducible kite pseudo BL-algebras and their classification
    • …
    corecore