Representation of modals

• Autorzy: Pilitowska A. , Zamojska-Dzienio A.
• Języki publikacji: EN

Abstrakty

EN

The main aim of this paper is to describe the free objects in arbitrary varieties of modals (semilattice ordered idempotent and entropic algebras)and give some new representations of modals.

Słowa kluczowe

EN

mode; modal; semilattice; free algebra; variety; class of algebras; identities; representation

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 3
• Strony: 535--556
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Pilitowska A.

autor

Zamojska-Dzienio A.

• Faculty Of Mathematics And Information Science Warsaw University Of Technology Plac Politechniki 1 00-661 Warsaw, Poland,

Bibliografia

• [1] K. Adaricheva, A. Pilitowska, D. Stanovskỳ, Complex algebras of subalgebras, Algebra Logic 47 (2008), 367–383.
• [2] S. N. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer Verlag, New York, 1981.
• [3] R. Freese, E. Kiss, M. Valeriote, UACalc, A Universal Algebra Calculator, http://www.uacalc.org/.
• [4] G. Gräzer, H. Lakser, Identities for globals (complex algebras) of algebras, Colloq. Math. 56 (1988), 19–29.
• [5] B. Jósson, A. Tarski, Boolean algebras with operators I, Amer. J. Math. 73 (1951), 891–939.
• [6] K. Kearnes, Semilattice modes I: the associated semiring, Algebra Universalis 34 (1995), 220–272.
• [7] A. I. Mal’cev, Algebraičeskie sistemy, [in Russian], Sovremennaja Algebra, Nauka, Moscow, 1970. English translation: Algebraic Systems, Springer Verlag, Berlin, 1973.
• [8] R. McKenzie, A. Romanowska, Varieties of · – distributive bisemilattices, Contributions to General Algebra 1 (1979), 213–218.
• [9] A. Pilitowska, Modes of submodes, Ph. D. Thesis, Warsaw University of Technology, Warsaw, Poland, 1996.
• [10] A. Pilitowska, A. Zamojska-Dzienio, On some congruences of power algebras, submitted. (http://www.mini.pw.edu.pl/~apili/APAZ310309.pdf)
• [11] K. J. Pszczoła, A. B. Romanowska, J. D. H. Smith, Duality for some free modes, Discuss. Math. Gen. Algebra Appl. 23 (2003), 45–62.
• [12] A. Romanowska, Semi-affine modes and modals, Sci. Math. Jpn. 61 (2005), 159–194.
• [13] A. Romanowska, B. Roszkowska, On some groupoid modes, Demonstratio Math. 20 (1987), 277–290.
• [14] A. B. Romanowska, J. D. H. Smith, Modal Theory, Heldermann Verlag, Berlin, 1985.
• [15] A. B. Romanowska, J. D. H. Smith, Modes, World Scientific, Singapore, 2002.
• [16] L. A. Shemetkov, A. Skiba, Formations of Algebraic Systems, [in Russian], Nauka, Moscow, 1989.
• [17] K. Ślusarska, Distributive differential modals, Discuss. Math. Gen. Algebra Appl. 28 (2008), 29–47.