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  1. No Access

    Chapter

    Varieties of Lattices

    In this chapter we discuss some of the more recent results and give a general overview of what is currently known about lattice varieties. Of course it is impossible to give a comprehensive account. Often we o...

    P. Jipsen, H. Rose in Lattice Theory: Special Topics and Applications (2016)

  2. No Access

    Article

    The Blok–Ferreirim theorem for normal GBL-algebras and its application

    Generalized basic logic algebras (GBL-algebras for short) have been introduced in [JT02] as a generalization of Hájek’s BL-algebras, and constitute a bridge between algebraic logic and ℓ-groups. In this paper ...

    P. Jipsen, F. Montagna in Algebra universalis (2009)

  3. No Access

    Article

    On the structure of generalized BL-algebras

    A generalized BL - algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities $$ x\Lambda y = ((x\Lambd...

    P. Jipsen, F. Montagna in algebra universalis (2006)

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    Article

    Cancellative residuated lattices

    Cancellative residuated lattices are natural generalizations of lattice-ordered groups ( \( \mathcal{l} \) -groups)...

    P. Bahls, J. Cole, N. Galatos, P. Jipsen, C. Tsinakis in algebra universalis (2003)

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    Article

    The variety generated by order algebras

    Every ordered set can be considered as an algebra in a natural way. We investigate the variety generated by order algebras. We prove, among other things, that this variety is not finitely based and, although ...

    R. Freese, J. Ježek, P. Jipsen, P. Marković, M. Maróti, R. McKenzie in algebra universalis (2002)

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    Chapter

    A Survey of Residuated Lattices

    Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices hav...

    P. Jipsen, C. Tsinakis in Ordered Algebraic Structures (2002)

  7. No Access

    Article

    Total tense algebras and symmetric semiassociative relation algebras

    It is well known that the latticeΛ RA of varieties of relation algebras has exactly three atoms. An unsolved problem, posed by B. Jónsson, is to determine the varieties of heig...

    P. Jipsen, R. L. Kramer, R. D. Maddux in algebra universalis (1995)

  8. No Access

    Article

    Small representations of the relation algebra ɛn+1(1, 2, 3)

    Applying combinatorial methods, we prove that the symmetric relation algebra ɛn+1(1, 2, 3) ofn+1 atoms is finitely representable for alln ≳ 1, on at most (2+o(1))n2 elements asn → ∞. We explicitly construct a rep...

    P. Jipsen, R. D. Maddux, Z. Tuza in algebra universalis (1995)

  9. No Access

    Article

    Adjoining units to residuated Boolean algebras

    We consider a varietyV ofr-algebras, — residuated Boolean algebras, — and ask under what conditions a memberA ofV can be embedded in a memberA' having a unit element. The answer, although quite simple, is somewha...

    P. Jipsen, B. Jónsson, J. Rafter in algebra universalis (1995)

  10. No Access

    Article

    Minimal relation algebras

    This paper is concerned with the covers of the atoms in the lattice of varieties of relation algebras. Aminimal relation algebra is one that is simple and generates such a subvariety. The main result we prove is ...

    P. Jipsen, E. Lukács in algebra universalis (1994)