algebra universalis

, Volume 12, Issue 1, pp 154–159 | Cite as

A lemma on flatness

  • B. Banaschewski
Article
  • 28 Downloads

Keywords

Direct Limit Algebra UNIV Galois Connection Proper Class Essential Extension 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. Banaschewski,Injectivity and essential extensions in equational classes of algebras, Queen's Papers Pure Appl. Math.25 (1970), 131–147.MathSciNetGoogle Scholar
  2. [2]
    B. Banaschewski,Sheaves of Banach spaces. Quaest. Math.2 (1977), 1–22.MATHMathSciNetGoogle Scholar
  3. [3]
    B. Banaschewski,Essential extensions of T 0-spaces. Gen. Top. Appl.7 (1977), 233–246.MATHMathSciNetGoogle Scholar
  4. [4]
    B. Banaschewski andG. Bruns,Categorical characterization of the MacNeille completion. Arch. der Math.18 (1967), 369–377.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    B. Banaschewski andE. Nelson,Tensor products and bimorphisms. Can. Math. Bull.19 (1976), 385–401.MATHMathSciNetGoogle Scholar
  6. [6]
    N. Bourbaki,Algèbre Commutative, Ch. I & II. Act. sci. et ind. 1290, Hermann, Paris 1961.Google Scholar
  7. [7]
    G. Bruns andH. Lakser,Injective hulls of semilattices. Can. Math. Bull.13 (1970), 115–118.MATHMathSciNetGoogle Scholar
  8. [8]
    S. Bulman-Fleming andK. McDowell,The category of mono-unary algebras. Alg. Univ. (to appear).Google Scholar
  9. [9]
    S. Bulman-Fleming andK. McDowell,Flat semilattices. Proc. Amer. Math. Soc.72 (1978), 228–232.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    S. Bulman-Fleming andK. McDowell,Flatness in varieties of normal bands (to appear).Google Scholar
  11. [11]
    H. B. Cohen,Injective envelopes of Banach spaces. Bull. Amer. Math. Soc.70 (1964), 723–726.MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    G. Grätzer,Universal Algebra. Van Nostrand, Princeton 1968.MATHGoogle Scholar
  13. [13]
    M. Kel'p,On homological classification of monoids. Siberian Math. J.13 (1972), 396–401.CrossRefGoogle Scholar
  14. [14]
    J. Lambek,A module is flat if and only if its character module is injective. Can. Math. Bull7 (1964), 237–243.MathSciNetMATHGoogle Scholar
  15. [15]
    J. Lambek,Lectures on rings and modules. Blaisdell, Toronto, 1966.MATHGoogle Scholar
  16. [16]
    D. Lazard,Author de la platitude. Bull. Soc. Math. France97 (1969), 81–128.MATHMathSciNetGoogle Scholar
  17. [17]
    S. Mac Lane,Categories for the working mathematician. Graduate Texts in Mathematics 5, Springer-Verlag, New York Heidelberg Berlin 1971.MATHGoogle Scholar
  18. [18]
    E. Nelson,Galois connections as left adjoint maps. Comm. Math. Univ. Carol.17 (1976), 523–541.MATHGoogle Scholar
  19. [19]
    D. Scott,Continuous lattices. LNM 274, 97–136. Springer-Verlag, Berlin-Heidelberg-New York, 1972.MATHGoogle Scholar
  20. [20]
    B. Stenström,Flatness and localization over monoids. Math. Nachr.48 (1970), 315–334.Google Scholar
  21. [21]
    B. Zimmermann,Endomorphismenringe von Selbstgeneratoren. Doctoral thesis. Munich, 1974.Google Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • B. Banaschewski
    • 1
  1. 1.McMaster UniversityHamiltonCanada

Personalised recommendations