PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2003 | 23 | 2 | 149-161
Tytuł artykułu

On the characterisation of Mal'tsev and Jónsson-Tarski algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework for the characterisation of Mal'tsev and Jónsson-Tarski algebras. Mal'tsev algebras are characterized by simplicial identities in the product complex of an algebra. In the dual of a pointed variety, a simplicial object known as the pointed complex is then constructed. The basic simplicial Mal'tsev identity in the pointed complex characterises Jónsson-Tarski algebras. Higher-dimensional simplicial Mal'tsev identities in the pointed complex are characteristic of a class of algebras lying properly between Goldie and Jónsson-Tarski algebras.
Twórcy
  • Department of Mathematics, Iowa State University, Ames, IA 50011, USA
Bibliografia
  • [1] J. Duskin, Simplicial Methods and the Interpretation of 'Triple' Cohomology, Mem. Amer. Math. Soc., No. 163, 1975.
  • [2] A.W. Goldie, On direct decompositions. I, and II, Proc. Cambridge Philos. Soc. 48 (1952), 1-34.
  • [3] M. Gran and M.C. Pedicchio, n-Permutable locally finite presentable categories, Theory Appl. Categ. 8 (2001), 1-15.
  • [4] H.-P. Gumm, Geometrical Methods in Congruence Modular Varieties, Mem. Amer. Math. Soc, No. 286. doi: 1983
  • [5] J. Hagemann and C. Herrmann, A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity, Arch. Math. (Basel) 32 (1979), 234-245.
  • [6] J. Hagemann and A. Mitscke, On n-permutable congruences, Algebra Universalis 3 (1973), 8-12.
  • [7] B. Jónsson and A. Tarski, Direct Decompositions of Finite Algebraic Systems, Notre Dame Mathematical Lectures, Notre Dame, IN, 1947.
  • [8] S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, New York, NY, 1971.
  • [9] A.I. Mal'tsev, K obshche teorii algebraicheskikh sistem, Mat. Sb. (N.S.) 35 (77) (1954), 3-20.
  • [10] A.I. Mal'cev, On the general theory of algebraic systems, (translation of [] by H. Alderson), Transl. Amer. Math. Soc. 27 (1963), 125-140.
  • [11] J.D.H. Smith, Mal'cev Varieties, Springer-Verlag, Berlin 1976.
  • [12] J.D.H. Smith, Centrality, Abstr. Amer. Math. Soc. 1 (1980), 774-A21.
  • [13] J.D.H. Smith and A.B. Romanowska, Post-Modern Algebra, Wiley, New York, NY, 1999.
  • [14] S.T. Tschantz, More conditions equivalent to congruence modularity, 'Universal Algebra and Lattice Theory,' Springer-Verlag, Berlin 1985, 270-282.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1070
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.