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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    MacDonald, Sheila Oates and Vaughan-Lee, M. R. 1978. Varieties that make one Cross. Journal of the Australian Mathematical Society, Vol. 26, Issue. 03, p. 368.
    Mendelsohn, N.S and Padmanabhan, R 1977. A polynomial map preserving the finite basis property. Journal of Algebra, Vol. 49, Issue. 1, p. 154.
    Taylor, Walter 1977. Contributions to Universal Algebra. p. 465.
    Clark, David M. and Krauss, Peter H. 1976. Para primal algebras. Algebra Universalis, Vol. 6, Issue. 1, p. 165.
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Various varieties1

  • Sheila Oates MacDonald (a1)
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The study of varieties of universal algebras2 which was initiated by Birkhoff in 1935, [2], has received considerable attention during the past decade; the question of particular interest being: “Which varieties have a finite basis for their laws?” In that paper Birkhoff showed that the laws of a finite algebra which involve a bounded number of variables are finitely based, so it is not altogether surprising that finite algebras have received their share of this attention.

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COPYRIGHT: © Australian Mathematical Society 1973
References
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[1]Baker, K. A., ‘Equational bases for finite algebras’ (Preliminary report), Notices Amer. Math. Soc. 19 (1972), 691–08–2.
[2]Birkhoff, G., ‘On the structure of abstract algebras’, Proc. Cambridge Phil. Soc. 31 (1935), 433–454.
[3]Cohn, P. M., Universal algebra (Harper & Row, New York, 1965).
[4]Day, A., ‘A characterization of modularity for congruence lattices of algebras’, Canad. Math. Bull. 12 (1969), 167–173.
[5]Evans, T., ‘Identical relations in loops’, J. Austral. Math. Soc. 12 (1971), 275–286.
[6]Jónsson, B., ‘Algebras whose congruence lattices are distributive’, Math. Scand. 21 (1967), 110–121.
[7]Kovács, L. G. and Newman', M. F., Cross varieties of groups', Proc. Roy. Soc. (London) A, 292 (1966), 530–536.
[8]Kruse, R. L., ‘Identities satisfied by a finite ring’, J. Algebra 26 (1973), 298–318.
[9]Lyndon, R. C., ‘Identities in two-valued calculi’, Trans. Amer. Math. Soc. 71 (1951), 457–465.
[10]Mal'cev, A. I., ‘On the general theory of algebraic systems’, Mat. Sb. (N. S.) 35 (77) (1954), 3–20.
[11]McKenzie, R., ‘Equational bases for lattice theories’, Math. Scand. 27 (1970), 24–38.
[12]Murskii, V. L., ‘The existence in three-valued logic of a closed class with finite basis, not having a finite complete system of identities’, Soviet Math. Doklady, 6 (1965), 1020–1024.
[13]Neumann, Hanna, Varieties of groups (Ergebaisse der Mathematik und ihrer Grenzgebiete, Bd. 37, Springer-Verlag, Berlin, 1967).
[14]Oates, Sheila and Powell, M. B., ‘Identical relations in finite groups’, J. Algebra 1 (1964), 11–39.
[15]Perkins, P., ‘Bases for equational theories of semigroups’, J. Algebra 11 (1969), 298–314.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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