Unary operations with long pre-periods

Ratanaprasert, C.; Denecke, Klaus

doi:10.1016/j.disc.2007.10.027

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…An operation f on A is connected if for each a, b ∈ A, there exist nonnegative integers n, m such that f n (a) = f m (b). Some results from [2] and [13] imply that λ(f ) ≤ |A|−1 and the authors characterized f with λ(f…”

Section: Introductionmentioning

confidence: 99%

The pre-period of the glued sum of finite modular lattices

Charoenpol¹,

Chotwattakawanit²

2023

Discuss. Math. - General Algebra and Applications

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The notion of a pre-period of an algebra A is defined by means of the notion of the pre-period λ(f ) of a monounary algebra A; f : it is determined by sup{λ(f ) | f is an endomorphism of A}. In this paper we focus on the pre-period of a finite modular lattice. The main result is that the pre-period of any finite modular lattice is less than or equal to the length of the lattice; also, necessary and sufficient conditions under which the pre-period of the glued sum is equal to the length of the lattice, are shown. Moreover, we show the triangle inequality of the pre-period of the glued sum.

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Section: Introductionmentioning

confidence: 99%

The pre-period of the glued sum of finite modular lattices

Charoenpol¹,

Chotwattakawanit²

2023

Discuss. Math. - General Algebra and Applications

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“…In [13], monounary algebras with a long pre-period were dealt with. A monounary algebra is said to be with a long pre-period if it is isomorphic to ({0, 1, .…”

Section: Remark 21ºmentioning

confidence: 99%

The endomorphism spectrum of a monounary algebra

Jakubíková-Studenovská

Potpinková

2014

Mathematica Slovaca

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ABSTRACT. The endomorphism spectrum spec A of an algebra A is defined as the set of all positive integers, which are equal to the number of elements in an endomorphic image of A, for all endomorphisms of A. In this paper we study finite monounary algebras and their endomorphism spectrum. If a finite set S of positive integers is given, one can look for a monounary algebra A with S = spec A. We show that for countably many finite sets S, no such A exists. For some sets S, an appropriate A with spec A = S are described.For n ∈ N it is easy to find a monounary algebra A with {1, 2, . . . , n} = spec A. It will be proved that if i ∈ N, then there exists a monounary algebra A such that spec A skips i consecutive (consecutive eleven, consecutive odd, respectively) numbers.Finally, for some types of finite monounary algebras (binary and at least binary trees) A, their spectrum is shown to be complete.

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All Congruence Modular Symmetric and Near-Symmetric Algebras

Ratanaprasert

Thiranantanakorn

2011

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Unary operations with long pre-periods

Cited by 3 publications

References 4 publications

The pre-period of the glued sum of finite modular lattices

The pre-period of the glued sum of finite modular lattices

The endomorphism spectrum of a monounary algebra

All Congruence Modular Symmetric and Near-Symmetric Algebras

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