Endomorphisms and subalgebras of Tarski algebras

• Autorzy: Gaitán H.

Identyfikatory

DOI

10.4467/20842589RM.15.002.3911

• Języki publikacji: EN

Abstrakty

EN

In this note we prove that a Tarski algebra is determined by the monoid of its endomorphisms as well as by the lattice of its subalgebras.

Słowa kluczowe

EN

implication algebra; Tarski algebra; monoid of endomorphisms

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2015
• Tom: Vol. 50
• Strony: 31--39
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Gaitán H.

• Departamento de Matem´aticas Facultad de Ciencias Universidad Nacional de Colombia Ciudad Universitaria, Bogot´a, Colombia

Bibliografia

• [1] M. Abad, D. Casta˜no and J. P. D´ıaz Varela, Zariski-type topology for implication algebras, Math. Log. Quart. 56:3 (2010), 299–309.
• [2] J. C. Abbott, Semi-Boolean algebras, Mat. Vesnik 19:4 (1967), 177–198.
• [3] S. A. Celani, L. M. Cabrer, Topological duality for Tarski algebras, Algebra Universalis 58 (2008), 73–94.
• [4] V. Koubek and H. Radovansk´a, Algebras determined by their endomorphism monoids. Cahiers de topologie et g´eom´etrie diff´erentielle cat´egoriques 35:3 (1994), 187–225.
• [5] H. Gait´an, Endomorphisms of impliaction algebras, Demostratio Math. Vol. XLVII, No 2 (2014), 284–288.
• [6] R. McKenzie and C. Tsinakis, On recovering a bounded distributive lattice from its endomorphism monoid, Houston Journal of Mathematicas 7:4 (1981), 525–529.
• [7] C. J. Maxon, On semigroups of Boolean ring endomorphism, Semigroup Forum 4 (1972), 78–82.
• [8] K. D. Magill, The semigroup of endomorphisms of a Boolean ring, it J. Austral. Math. Soc. 11 (1970), 411–416.
• [9] H. Rasiowa, An algebraic approach to non-classical logics, North Holland, Studies in Logic and the Foundations of Mathematicas, Vol 78, Amsterdam, 1974.
• [10] D. Sachs, The lattice of subalgebras of a Boolean algebra, Canad. J. Math. 14 (1962), 451–460.
• [11] B. M. Schein, Ordered sets, semilattices, distributive lattices and Boolean algebras with homomorphic endomorphism semigroups, Fund. Math. 68 (1970), 31–50.