Geodesic
Flocks in universal and Boolean algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 45-69.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: combinators, elementary functions, closure system, interpolators, semi-affine lattice 
@article{DMGAA_2010_30_1_a2,
     author = {Ricci, Gabriele},
     title = {Flocks in universal and {Boolean} algebras},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {45--69},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a2/}
}
TY  - JOUR
AU  - Ricci, Gabriele
TI  - Flocks in universal and Boolean algebras
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2010
SP  - 45
EP  - 69
VL  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a2/
LA  - en
ID  - DMGAA_2010_30_1_a2
ER  - 
%0 Journal Article
%A Ricci, Gabriele
%T Flocks in universal and Boolean algebras
%J Discussiones Mathematicae. General Algebra and Applications
%D 2010
%P 45-69
%V 30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a2/
%G en
%F DMGAA_2010_30_1_a2
Ricci, Gabriele. Flocks in universal and Boolean algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 45-69. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a2/

[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