Halušková, Emília Strong endomorphism kernel property for monounary algebras. (English) Zbl 1463.08003 Math. Bohem. 143, No. 2, 161-171 (2018). An endomorphism of an algebra \(A\) is called strong if it is compatible with all congruences on \(A\). If every congruence on \(A\) is a kernel of some strong endomorphism, then \(A\) is said to have a strong endomorphism kernel property (SEKP for short). If in this definition we exclude the universal congruence \(A^2\), then this weaker property is denoted by wSEKP. The author characterizes all monounary algebras having SEKP and those having wSEKP. Reviewer: Ivan Chajda (Přerov) Cited in 1 Document MSC: 08A30 Subalgebras, congruence relations 08A35 Automorphisms and endomorphisms of algebraic structures 08A60 Unary algebras Keywords:strong endomorphism; congruence; kernel; connected monounary algebra PDF BibTeX XML Cite \textit{E. Halušková}, Math. Bohem. 143, No. 2, 161--171 (2018; Zbl 1463.08003) Full Text: DOI References: [1] Blyth, T. S.; Fang, J.; Wang, L.-B., The strong endomorphism kernel property in distributive double p-algebras, Sci. Math. Jpn. 76 (2013), 227-234 · Zbl 1320.06009 [2] Blyth, T. S.; Silva, H. J., The strong endomorphism kernel property in Ockham algebras, Commun. Algebra 36 (2008), 1682-1694 · Zbl 1148.06005 [3] Fang, G.; Fang, J., The strong endomorphism kernel property in distributive p-algebras, Southeast Asian Bull. Math. 37 (2013), 491-497 · Zbl 1299.06017 [4] Fang, J.; Sun, Z.-J., Semilattices with the strong endomorphism kernel property, Algebra Univers. 70 (2013), 393-401 · Zbl 1305.06004 [5] Guričan, J., Strong endomorphism kernel property for Brouwerian algebras, JP J. Algebra Number Theory Appl. 36 (2015), 241-258 · Zbl 1333.06025 [6] Guričan, J.; Ploščica, M., The strong endomorphism kernel property for modular p-algebras and for distributive lattices, Algebra Univers. 75 (2016), 243-255 · Zbl 1348.06008 [7] Jakubíková-Studenovská, D.; Pócs, J., Monounary Algebras, Pavol Jozef Šafárik University, Košice (2009) · Zbl 1181.08001 [8] McKenzie, R. N.; McNulty, G. F.; Taylor, W. F., Algebras, Lattices, Varieties. Vol. 1, The Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole Advance Books & Software XII. Monterey, California (1987) · Zbl 0611.08001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.