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2012 | 10 | 3 | 987-1003
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On some congruences of power algebras

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EN
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EN
In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class of non-trivial subvarieties of the variety of all semilattice ordered modes (modals).
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Bibliografia
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  • [8] Kearnes K., Semilattice modes I: the associated semiring, Algebra Universalis, 1995, 34(2), 220–272 http://dx.doi.org/10.1007/BF01204784
  • [9] McKenzie R.N., McNulty G., Taylor W., Algebras, Lattices, Varieties. I, Wadsworth Brooks/Cole Math. Ser., Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, 1987
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  • [11] Pilitowska A., Modes of Submodes, PhD thesis, Warsaw University of Technology, 1996
  • [12] Pilitowska A., Zamojska-Dzienio A., Representation of modals, Demonstratio Math., 2011, 44(3), 535–556
  • [13] Pilitowska A., Zamojska-Dzienio A., Varieties generated by modes of submodes, preprint available at http://www.mini.pw.edu.pl/~apili/publikacje.html
  • [14] Romanowska A., Semi-affine modes and modals, Sci. Math. Jpn., 2005, 61(1), 159–194
  • [15] Romanowska A.B., Roszkowska B., On some groupoid modes, Demonstratio Math., 1987, 20(1–2), 277–290
  • [16] Romanowska A.B., Smith J.D.H., Bisemilattices of subsemilattices, J. Algebra, 1981, 70(1), 78–88 http://dx.doi.org/10.1016/0021-8693(81)90244-1
  • [17] Romanowska A.B., Smith J.D.H., Modal Theory, Res. Exp. Math., 9, Heldermann, Berlin, 1985
  • [18] Romanowska A.B., Smith J.D.H., Subalgebra systems of idempotent entropic algebras, J. Algebra, 1989, 120(2), 247–262 http://dx.doi.org/10.1016/0021-8693(89)90197-X
  • [19] Romanowska A.B., Smith J.D.H., On the structure of subalgebra systems of idempotent entropic algebras, J. Algebra, 1989, 120(2), 263–283 http://dx.doi.org/10.1016/0021-8693(89)90198-1
  • [20] Romanowska A.B., Smith J.D.H., Modes, World Scientific, River Edge, 2002
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0018-6
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