Skip to main content
Log in

Families of algebras with unique (sub-) direct factorization: Equational characterization of factorization

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

  1. Foster, A. L.: Functional completeness in the small. Algebraic structure theorems and identities. Math. Ann.143, 29–58 (1961).

    Google Scholar 

  2. —— Functional completeness in the small, II. Algebraic cluster theorem. Math. Ann.148, 173–191 (1962).

    Google Scholar 

  3. —— The identities of — and unique factorization within — certain classes of universal algebras. Math. Z.62, 171–188 (1955).

    Google Scholar 

  4. —— Generalized “Boolean” theory of universal algebras. Part I: Subdirect sums and normal representation theorem. Math. Z.58, 306–336 (1953). Part II: Identities and subdirect sums of functionally complete algebras. Math. Z.59, 191–199 (1953).

    Google Scholar 

  5. —— andA. Pixley: Semi-categorical algebras, I. Semi-primal algebras. Math. Z.83, 147–169 (1964).

    Google Scholar 

  6. ———— Semi-categorical algebras, II. Math. Z.85, 169–184 (1964).

    Google Scholar 

  7. Pixley, A.: Distributivity and permutability of congruence relations in equational classes of algebras. Proc. Am. Math. Soc.14, 105–109 (1963).

    Google Scholar 

  8. O'Keefe, E.: Primal clusters of two-element algebras. Pac. J. Math.11, 1505–1510 (1961).

    Google Scholar 

  9. —— On the independence of primal algebras. Math. Z.73, 79–84 (1960).

    Google Scholar 

  10. Sioson, F. M.: Contributions to primal algebra theory and independence. Doctoral dissertation, Univ. of Calif. (Berkeley) 1960.

    Google Scholar 

  11. —— Some primal clusters. Math. Z.75, 201–210 (1961).

    Google Scholar 

  12. Astromoff, A.: Functionally complete algebras and their generalizations. Doctoral Dissertation, Univ. of Calif. (Berkeley) 1963.

    Google Scholar 

  13. Krull, W.: Subdirekte Summendarstellung von Integritätsbereichen. Math. Z.52, 810–826 (1950).

    Google Scholar 

  14. Birkhoff, G.: Subdirect unions in universal algebras. Bull. Am. Math. Soc.50, 764–768 (1944).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Foster, A.L. Families of algebras with unique (sub-) direct factorization: Equational characterization of factorization. Math. Ann. 166, 302–326 (1966). https://doi.org/10.1007/BF01360786

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01360786

Keywords

Navigation