Annali dell’Università di Ferrara

, Volume 17, Issue 1, pp 35–42 | Cite as

Sulle classi filtrali di algebre

  • George M. Bergman


Generalizing results of [1], we show that if a classK of algebras is filtral (as defined byMagari [1]), then so is the class of all simple algebras in the varietyW K generated byK, and these simple objects are precisely all subalgebras of all ultraproducts of copies of algebras inK. All algebras inW K are semisimple and regular. We then obtain charac terizations of filtral and semifiltral classes of algebras in terms of the existence of certain types of operations in these algebras, and illustrate our results with examples, mainly from ring theory.


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Testi Citati

  1. [1]
    R. Magari,Varietà a quozienti filtrali, Annali dell'Università di Ferrara (N.S.), XIV 1969, n. 2, pp. 5–20.MathSciNetGoogle Scholar
  2. [2]
    S. Endo,Note on p.p. rings (A supplement to Hattori's paper), Nagoya Math. J., 17 (1960), 167–170.MATHMathSciNetGoogle Scholar
  3. [3]
    G. M. Bergman,Commutative hereditary rings and centers of hereditary rings, Proc. Lond. Math. Soc. (3) 23 (1971), 214–236.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    R. S. Pierce,Modules over Commutative Regular Rings, Mem. A.M.S., n. 70 (1967).Google Scholar
  5. [5]
    R. Franci eL. Toti-Rigatelli,Sulla varietà dei reticoli distributivi, Annali dell'Università di Ferrara (N.S.), XIV (1969), n. 4, pp. 23–27.MathSciNetGoogle Scholar
  6. [6]
    R. Magari,Costruzione di classi filtrali, Annali dell'Università di Ferrara (N.S.), XIV (1969), n. 6, pp. 35–52.MathSciNetGoogle Scholar

Copyright information

© Università degli Studi di Ferrara 1972

Authors and Affiliations

  • George M. Bergman
    • 1
  1. 1.Department of MathematicsHarward UniversityCambridgeUSA

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