2005
DOI: 10.1007/s10587-005-0011-3
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On a representation of monounary algebras

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Cited by 3 publications
(5 citation statements)
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“…The first goal of this paper is, for a given monounary algebra (A, f ), a characterization of all monounary algebras (A, g) such that the algebras (A, f ) and (A, g) have the same sets of quasiorders. This problem is in a close connection with the papers [3]- [6], where similar problems were investigated for congruences or endomorphisms, respectively.…”
Section: Introductionsupporting
confidence: 52%
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“…The first goal of this paper is, for a given monounary algebra (A, f ), a characterization of all monounary algebras (A, g) such that the algebras (A, f ) and (A, g) have the same sets of quasiorders. This problem is in a close connection with the papers [3]- [6], where similar problems were investigated for congruences or endomorphisms, respectively.…”
Section: Introductionsupporting
confidence: 52%
“…First let us recall some results of [5] and [6] which will be applied in this section (they are denoted by the numbers of the corresponding assertions in [5] and [6]). The notations introduced here will be used also in the following section without other quotation.…”
Section: Same Quasiordersmentioning
confidence: 99%
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“…The author [5]- [10] dealt with these relations for monounary algebras. Let us denote by U (and U c , respectively) the class of all (all connected) monounary algebras.…”
Section: Introductionmentioning
confidence: 99%
“…Next, in [6] all connected monounary algebras retract irreducible in the class U were found. In [10] it was proved that there exist connected monounary algebras which are not representable by means of connected monounary algebras which are retract irreducible in U c . An analogous result was shown for the representability in U .…”
Section: Introductionmentioning
confidence: 99%