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On free modes

Michał Marek Stronkowski (2006)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem describing the equational theory of all modes of a fixed type. We use this result to show that a free mode with at least one basic operation of arity at least three, over a set of cardinality at least two, does not satisfy identities selected by ’A. Szendrei in Identities satisfied by convex linear forms, Algebra Universalis 12 (1981), 103–122, that hold in any subreduct of a semimodule over a commutative semiring. This gives a negative answer to the question raised by A. Romanowska:...

On free Turing algebras

Herbert Lugowski (1986)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

On hyperplanes and semispaces in max–min convex geometry

Viorel Nitica, Sergeĭ Sergeev (2010)

Kybernetika

The concept of separation by hyperplanes and halfspaces is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry are based on semispaces. This paper answers the question which semispaces are hyperplanes and when it is possible to “classically” separate by hyperplanes in max-min convex geometry.

On ideal extensions of partial monounary algebras

Danica Jakubíková-Studenovská (2008)

Czechoslovak Mathematical Journal

In the present paper we introduce the notion of an ideal of a partial monounary algebra. Further, for an ideal ( I , f I ) of a partial monounary algebra ( A , f A ) we define the quotient partial monounary algebra ( A , f A ) / ( I , f I ) . Let ( X , f X ) , ( Y , f Y ) be partial monounary algebras. We describe all partial monounary algebras ( P , f P ) such that ( X , f X ) is an ideal of ( P , f P ) and ( P , f P ) / ( X , f X ) is isomorphic to ( Y , f Y ) .

On ideals and congruences in BCC-algebras

Wiesław Aleksander Dudek, Xiaohong Zhang (1998)

Czechoslovak Mathematical Journal

We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.

On ideals in De Morgan residuated lattices

Liviu-Constantin Holdon (2018)

Kybernetika

In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal...

On idempotent modifications of M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an M V -algebra 𝒜 we denote by 𝒜 ' , A and ℓ ( 𝒜 ) the idempotent modification, the underlying set or the underlying lattice of 𝒜 , respectively. In the present paper we prove that if 𝒜 is semisimple and ℓ ( 𝒜 ) is a chain, then 𝒜 ' is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.

Currently displaying 101 – 120 of 323