PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2010 | 30 | 1 | 45-69
Tytuł artykułu

Flocks in universal and Boolean algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients.
The main example, we consider outside vector spaces, concerns Boolean algebras, where flocks form "local" algebras with a sparseness similar to the one of vector spaces. We also outline the problem of generalizing the Segre transformations of based algebras, which used certain flocks, in order to approach a general transformation notion.
Rocznik
Tom
30
Numer
1
Strony
45-69
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-04-17
poprawiono
2009-12-20
Twórcy
  • Universitá di Parma, Dipart. di Matematica, I-43100 Parma, Italy
Bibliografia
  • [1] R. Baer, Linear Algebra and Projective Geometry (Academic Press, New York 1952).
  • [2] H. B. Curry and R. Feys, Combinatory Logic, Vol. I, (North-Holland, Amsterdam 1958).
  • [3] K. Denecke and S.L. Wismath, Hyperidentities and Clones (Gordon and Breach Science Publishers, Amsterdam 2000).
  • [4] K. Denecke, Menger algebras and clones of terms. East-West J. Math. 5 (2) (2003), 179-193.
  • [5] K. Głazek, Algebras of Operations, in A.G. Pinus and K.N. Ponomaryov, Algebra and Model Theory 2 (Novosibirsk, 1999) 37-49.
  • [6] J.D. Monk, Introduction to Set Theory (McGraw-Hill, New York 1969).
  • [7] G. Ricci, P-algebras and combinatory notation, Riv. Mat. Univ. Parma 5(4) (1979), 577-589.
  • [8] G. Ricci, Universal eigenvalue equations, Pure Math. and Appl. Ser. B, 3, 2-3-4 (1992), 231-288. (Most of the misprints appear in ERRATA to Universal eigenvalue equations, Pure Math. and Appl. Ser. B, 5, 2 (1994), 241-243. Anyway, the original version is in http://www.cs.unipr.it/~ricci/)
  • [9] G. Ricci, Two isotropy properties of 'universal eigenspaces' (and a problem for DT0L rewriting systems), in G. Pilz, Contributions to General Algebra 9 (Verlag Hölder-Pichler-Tempsky, Wien 1995 - Verlag B.G. Teubner), 281-290.
  • [10] G. Ricci, Some analytic features of algebraic data, Discrete Appl. Math. 122/1-3 (2002), 235-249. doi: 10.1016/S0166-218X(01)00323-7
  • [11] G. Ricci, A semantic construction of two-ary integers, Discuss. Math. Gen. Algebra Appl. 25 (2005), 165-219. doi: 10.7151/dmgaa.1099
  • [12] G. Ricci, Dilatations kill fields, Int. J. Math. Game Theory Algebra, 16 5/6 (2007), 13-34.
  • [13] G. Ricci, All commutative based algebras have endowed dilatation monoids, (to appear on Houston J. of Math.).
  • [14] G. Ricci, Another characterization of vector spaces without fields, in G. Dorfer, G. Eigenthaler, H. Kautschitsch, W. More, W.B. Müller. (Hrsg.): Contributions to General Algebra 18. Klagenfurt: Verlag Heyn GmbH & Co KG, 31 February 2008, 139-150.
  • [15] G. Ricci, Transformations between Menger systems, Demonstratio Math. 41 (4) (2008), 743-762.
  • [16] G. Ricci, Sameness between based universal algebras, Demonstratio Math. 42 (1) (2009), 1-20.
  • [17] M. Steinby, On algebras as tree automata, Colloquia Mathematica Societatis János Bolyai, 17. Contributions to Universal Algebra, Szeged (1975), 441-455.
  • [18] B. Vormbrock and R. Wille, Semiconcept and Protoconcept Algebras: The Basic Theorems, in B. Ganter, G. Stumme & R. Wille (eds.), Formal Concept Analysis: Foundations and Applications, (Springer-Verlag, Berlin 2005). doi: 10.1007/11528784₂
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1162
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.