Endomorphisms and subalgebras of Tarski algebras
Choose format
RIS BIB ENDNOTEEndomorphisms and subalgebras of Tarski algebras
Publication date: 21.10.2015
Reports on Mathematical Logic, 2015, Number 50, pp. 31-39
https://doi.org/10.4467/20842589RM.15.002.3911Authors
Endomorphisms and subalgebras of Tarski algebras
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.
[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. Gaita´n, 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.
Information: Reports on Mathematical Logic, 2015, Number 50, pp. 31-39
Article type: Original article
Universidad Nacional de Colombia Ciudad Universitaria, Bogota, Colombia
Published at: 21.10.2015
Article status: Open
Licence: None
Percentage share of authors:
Article corrections:
-Publication languages:
English