Retract irreducibility of monounary algebras (original) (raw)

Retract irreducibility of connected monounary algebras II

Czechoslovak Mathematical Journal

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DR-irreducibility of connected monounary algebras

Czechoslovak Mathematical Journal, 2000

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

On a cancellation law for monounary algebras

Mathematica Bohemica

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Test elements and the retract theorem for monounary algebras

Czechoslovak Mathematical Journal, 2007

On a representation of monounary algebras

Czechoslovak Mathematical Journal, 2005

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Antiatomic retract varieties of monounary algebras

Czechoslovak Mathematical Journal

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Partially-2-Homogeneous Monounary Algebras

Czechoslovak Mathematical Journal, 2000

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Some properties of retract lattices of monounary algebras

Mathematica Slovaca, 2012

Necessary and sufficient conditions for a connected monounary algebra (A, f), under which the lattice R ∅(A, f) of all retracts of (A, f) (together with ∅) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of R ∅(A, f) are characterized. Further, there are described all connected monounary algebras (A, f) such that the lattice R ∅(A, f) is complemented. In this case R ∅(A, f) forms a boolean lattice.

On 2-Homogeneity of Monounary Algebras

Czechoslovak Mathematical Journal

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Lattice of retracts of monounary algebras

Mathematica Slovaca, 2011

We investigate lattices of retracts of monounary algebras. Semimodularity and concepts related to semimodularity (M-symmetry and Mac Lane's condition) are dealt with. Further, we give a description of all connected monounary algebras with modular retract lattice. c 2011 Mathematical Institute Slovak Academy of Sciences 2000 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 08A60. K e y w o r d s: monounary algebra, retract, lattice of retracts.

On completions of partial monounary algebras

Czechoslovak Mathematical Journal

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On finite retract lattices of monounary algebras

Mathematica Slovaca, 2012

For a monounary algebra (A, f ) we denote R ∅ (A, f ) the system of all retracts (together with the empty set) of (A, f ) ordered by inclusion. This system forms a lattice. We prove that if (A, f ) is a connected monounary algebra and R ∅ (A, f ) is finite, then this lattice contains no diamond. Next distributivity of R ∅ (A, f ) is studied. We find a representation of a certain class of finite distributive lattices as retract lattices of monounary algebras. c 2012 Mathematical Institute Slovak Academy of Sciences 2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 08A60. K e y w o r d s: monounary algebra, retract, lattice of retracts.

IRREDUCIBLE QUASIORDERS OF MONOUNARY ALGEBRAS

Journal of the Australian Mathematical Society, 2013

Rooted monounary algebras can be considered as an algebraic counterpart of directed rooted trees. We work towards a characterization of the lattice of compatible quasiorders by describing its join-and meet-irreducible elements. We introduce the limit B∞ of all d-dimensional Boolean cubes 2 d as a monounary algebra; then the natural order on 2 d is meet-irreducible. Our main result is that any completely meet-irreducible quasiorder of a rooted algebra is a homomorphic preimage of the natural partial order (or its inverse) of a suitable subalgebra of B∞. For a partial order, it is known that complete meet-irreducibility means that the corresponding partially ordered structure is subdirectly irreducible. For a rooted monounary algebra it is shown that this property implies that the unary operation has finitely many nontrivial kernel classes and its graph is a binary tree.

Retracts of monounary algebras corresponding to groupoids

Mathematica Slovaca

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On ideal extensions of partial monounary algebras

Czechoslovak Mathematical Journal, 2008

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