Transformations between Menger system

• Autorzy: Ricci G.
• Języki publikacji: EN

Abstrakty

EN

To define transformations between based universal algebras we must introduce representations that depend on the bases, contrary to what was possible for general vector spaces and believed possible for universal algebras. In fact, a counterex-ample shows that by representation-free transformations alone one cannot even ascertain whether a universal algebra has any dimension or not. A transformation notion, which can do, concerns basis dependent Menger systems. It enjoys a basic geometric property of universal algebras, the preservation of reference flocks, and generalizes the transformation groups of Linear Algebra into groupoids.

Słowa kluczowe

EN

universal matrix; general isomorphisms; Menger system

PL

grupy przekształceń; izomorfizm ogólny; macierz uniwersalna; system Mengera

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 4
• Strony: 743--762
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Ricci G.

• Universita di Parma, Dipart. di Mathematica, I-43100 Parma, Italy,

Bibliografia

• [1] K. Denecke, Menger algebras and clones of terms, East-West J. Math. 5 (2) (2003), 179-193.
• [2] K. Glazek, Morphisms of general algebras without fixed fundamental operations, Contemp. Math. 184 (1995), 117-137.
• [3] A. Goetz and C. Ryll - Nardzewski, On bases of abstract algebras, Bull. Acad. Polon. Sci. S ́er. Sci. Math. Astr. Phys. 8 (1960), 157-161.
• [4] G. Gratzer, Universal Algebra, 2th ed., SpringerVerlag, New York-Heidelberg, 1979.
• [5] J. D. Monk, Introduction to Set Theory, McGraw-Hill Book Co., New York-London-Sydney 1969.
• [6] G. Ricci,Universal eigenvalue equations, Pure Math. Appl. Ser. B 3 (1992), 2-4, 231-288 (1993). (Most of the misprints appear in ERRATA to Universal eigenvalue equations, Pure Math. Appl. Ser. B, 5, (1994), 2, 241-243. Anyway, the original version is in www.cs.unipr.it/ ̃ricci/).
• [7] G. Ricci, Two isotropy properties of “universal eigenspaces” (and a problem for DT0L rewriting systems), Contributions to general algebra, 9 (Linz, 1994), 281-290,Holder-Pichler-Tempsky, Vienna, 1995.
• [8] G. Ricci, New characterizations of universal matrices show that neural networks cannot be made algebraic, Contributions to general algebra, 10 (Klagenfurt, 1997), 269-291, Heyn, Klagenfurt, 1998.
• [9] G. Ricci, Some analytic features of algebraic data, Discrete Appl. Math. 122 (2002), 1-3, 235-249.
• [10] G. Ricci, Analytic monoids versus abstract monoids, Ital. J. Pure Appl. Math. 16 (2004), 125-136.
• [11] G. Ricci, Sameness between based universal algebras (transformations for Menger systems and analytic monoids), (Quaderni del Dipartimento di Matematica 456, Universit ́a di Parma, Parma, 2006) available at www.cs.unipr.it/ ̃ricci/.
• [12] G. Ricci, Dilatations kill fields, Int. J. Math. Game Theory Algebra, 16 (2007), 5-6,13-34.
• [13] G. Ricci, Another characterization of vector spaces without fields, in G. Dorfer, G. Eigenthaler, H. Kautschitsch, W. More, W. B. Muller. (Hrsg.): Contributions to General Algebra 18. Klagenfurt: Verlag Heyn GmbH & Co KG, 31. February 2008,139-150.
• [14] C. Segre, Un nuovo campo di ricerche geometriche, Atti Acad. Sci. Torino, Cl. Sci. Fis. Mat. Natur. 25 (1889), 276-301.