2014
DOI: 10.2478/s12175-014-0233-7
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The endomorphism spectrum of a monounary algebra

Abstract: 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 de… Show more

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Cited by 4 publications
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“…An endomorphism f of a structure A can be considered as a unary operation and A; f is a monounary algebra. Some properties of monounary algebras connected with the notion of homomorphism were studied, e.g., in [3,4,7,11,12].…”
Section: Introductionmentioning
confidence: 99%
“…An endomorphism f of a structure A can be considered as a unary operation and A; f is a monounary algebra. Some properties of monounary algebras connected with the notion of homomorphism were studied, e.g., in [3,4,7,11,12].…”
Section: Introductionmentioning
confidence: 99%