Abstract: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.
“…Assume that (c2) is valid and that A is not irreducible. By 1.3, there are a, b ∈ A with a = b such that f (a) = f (b) = c. Then the condition (C4) from [4] is satisfied and in view of the construction 4.1 and the corresponding lemmas in [4] we obtain that A is representable by means of irreducibles (these irreducibles are isomorphic to $ ∞ ).…”
Section: A With a One-element Cyclementioning
confidence: 96%
“…Connected monounary algebras which are retract irreducible in the above classes were characterized in [4], [5] and [6] as follows:…”
Section: Preliminariesmentioning
confidence: 99%
“…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%
“…In [5] and [4] all connected monounary algebras which are retract irreducible in the class U c were described. Next, in [6] all connected monounary algebras retract irreducible in the class U were found.…”
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 .…”
“…Assume that (c2) is valid and that A is not irreducible. By 1.3, there are a, b ∈ A with a = b such that f (a) = f (b) = c. Then the condition (C4) from [4] is satisfied and in view of the construction 4.1 and the corresponding lemmas in [4] we obtain that A is representable by means of irreducibles (these irreducibles are isomorphic to $ ∞ ).…”
Section: A With a One-element Cyclementioning
confidence: 96%
“…Connected monounary algebras which are retract irreducible in the above classes were characterized in [4], [5] and [6] as follows:…”
Section: Preliminariesmentioning
confidence: 99%
“…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%
“…In [5] and [4] all connected monounary algebras which are retract irreducible in the class U c were described. Next, in [6] all connected monounary algebras retract irreducible in the class U were found.…”
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 .…”
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.