Abstract
An endomorphism on an algebra \({\cal A}\) is said to be strong if it is compatible with every congruence on \({\cal A}\). If every congruence on \({\cal A}\), other than the universal congruence, is the kernel of a strong endomorphism on \({\cal A}\), then \({\cal A}\) is said to have the strong endomorphism kernel property. In this paper, we shall give a complete description of the structure of those symmetric extended MS-algebras that have this property via Priestley duality.
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References
Blyth, T. S., Varlet, J. S.: Ockham Algebras, Oxford University Press, Oxford, 1994
Blyth, T. S., Fang, J.: Extended Ockham algebras. Comm. Algebra, 28(3), 1271–1284 (2000)
Blyth, T. S., Fang, J.: Symmetric extended Ockham algebras. Algebra Colloquium, 10(4), 479–489 (2003)
Blyth, T. S., Silva, H. J.: The strong endomorphism kernel property in Ockham algebras. Comm. Algebra, 36(5), 1682–1694 (2008)
Blyth, T. S., Fang, J., Wang, L. B.: The strong endomorphism kernel property in distributive double p-algebras. Scientiae Mathematicae Japonicae, 76(2), 227–234 (2013)
Davey, B. A., Priestley, H. A.: Introduction to Lattices and Order, 2nd., Cambridge University Press, Cambridge, 2002
Fang, G., Fang, J.: The strong endomorphism kernel property in distributive p-algebras. Southeast Asian Bull. Math., 37(4), 491–497 (2013)
Fang, J.: Distributive Lattices with Unary Operations, Science Press, Beijing, 2011
Fang, J.: The strong endomorphism kernel property in double MS-algebras. Studia Logica, 105(5), 995–1013 (2017)
Fang, J.: The balanced pseudocomplemented Ockham algebras with the strong endomorphism kernel property. Studia Logica, 107(6), 1261–1277 (2019)
Fang, J., Sun, Z. J.: Semilattices with the strong endomorphism kernel property. Algebra Universalis, 70(4), 393–401 (2013)
Fang, J., Sun, Z. J.: Finite abelian groups with the strong endomorphism kernel property. Acta Math. Sinica, English Series, 36(9), 1076–1082 (2020)
Guričan, J.: Strong endomorphism kernel property for Brouwerian algebras. JP J. Algebras Number Theory Appl., 36(3), 241–258 (2015)
Guričan, J., Ploščica, M.: The strong endomorphism kernel property for modular p-algebras and for distributive lattices. Algebra Universalis, 75, 243–255 (2016)
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Fang, J. Symmetric Extended MS-algebras with the Strong Endomorphism Kernel Property. Acta. Math. Sin.-English Ser. 38, 1447–1458 (2022). https://doi.org/10.1007/s10114-022-1302-4
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DOI: https://doi.org/10.1007/s10114-022-1302-4