References
Andréka, H., B. Jónsson and L. Németi, Free algebras in discriminator varieties, to appear.
Bergman, G., Hyperidentities of groups and semigroups,Aequationes Mathematicae 23 (1981), 50–56.
Char, B. W., K. O. Geddes, G. H. Gonnet, M. B. Monagan and S. M. Watt,Maple Reference Manual (5th edition), WATCOM Publications Ltd., 1988.
Denecke, K. and R. Pöschel, A characterization of Sheffer functions by hyperidentities,Semigroup Forum 37 (1988), 351–362.
Freese, R., The variety of modular lattices is not generated by its finite members,Transactions of the American Mathematical Society 255 (1979), 277–300.
—, Free modular lattices,Transactions of the American Mathematical Society 261 (1980), 81–91.
Freese, R. S., R. N. McKenzie, G. F. McNulty and W. F. Taylor,Algebras, Lattices, Varieties, Volume 2, Wadsworth and Brooks-Cole Publishing Company, Monterey, CA, in preparation.
Graczyńska, E., On connections between identities and hyperidentities, Bulletin of the section of logic (Polish Academy of Sciences), 18 (1989), 25–32.
Graczyńska, E. and D. Schweigert, Hyperidentities of a given type,Algebra Universalis, to appear.
Herrmann, C., On the word problem for the modular lattice with four free generators, Math. Ann. 265 (1983), 513–527.
Jastrzebowski, W.,Slang Programming Language Manual, preprint, Toronto, © 1988.
Kim, K. H.,Boolean Matrix Theory and Applications, Volume 70 ofMonographs and Textbooks in Pure and Applied Mathematics Marcel Dekker, New York, 1982.
Kruse, R. L., Identities satisfied by a finite ring,J. Algebra 26 (1973) 298–318.
Lausch, H. and W. Nöbauer,Algebra of Polynomials, Volume 5 of theNorth-Holland Mathematical Library North-Holland, Amsterdam, 1973.
L'vov, I. V., Varieties of associative rings I, II,Algebra i Logika 12 (1973) 269–297, 667–688.
Mal'tsev, Yu. N. and E. N. Kuz'min, A basis for the identities of the algebra of second-order matrices over a finite field,Algebra i Logika 17 (1978), 28–32. English translation appears asAlgebra and Logic 17 (1978), 18–21.
Markowsky, G., Bounds on the index and period of binary relations on a finite set,Semigroup Forum 13 (1976), 253–260.
McKenzie, R. N., G. F. McNulty and W. F. Taylor,Algebras, Lattices, Varieties, Volume 1, Wadsworth and Brooks-Cole Publishing Company, Monterey, CA, 1987.
Movsisyan, Yu. M.,Introduction to the theory of algebras with hyperidentities, 240 pages, Erevan University, Erevan, 1986. (Vvedenie v teoriyu algebr so sverxtozhdestvami.) (Math Reviews 88f:08001). {The reader is encouraged to look at the review; it appears that the book has little to do with what we are doing here, but a detailed reading would be required to make absolutely sure.}
Neumann, W. D., Mal'cev conditions, spectra and Kronecker product,Journal of the Australian Mathematical Society (A) 25 (1978), 103–117.
Niven, I. Fermat's Theorem for matrices,Duke Mathematics Journal 15 (1948), 823–826.
Padmanabhan, R. and P. Penner, Bases of hyperidentities of lattices and semilattices, C. R. Math. Rep. Acad. Sci. Canada 4 (1982), #1, 9–14.
Padmanabhan, R., On some syntactical transforms of binary identities (to appear).
Padmanabhan, R. Subdirectly irreducible n-quasilattices, AMS Abstracts, 89T-06-98, 10 (1989), 257–258.
Padmanabhan, R. Equational theory of point algebras
Penner, P.,Hyperidentities of lattices, semilattices and diagonal semigroups, Ph. D. Thesis, University of Manitoba, Winnipeg, 1980.
—, Hyperidentities of lattices and semilattices,Algebra Universalis 13 (1981), 307–314.
— Hyperidentities of semilattices,Houston Journal of Mathematics 10 (1984), 81–108.
Petrov, A. N., On the injection rank of varieties of semigroups, Izvestiya VUZ. Matemika, 29 (1985), No. 11, 82–84. English translation: Izvestiya VUZ., Allerton Press, 114–117.
Pixley, A. F., The ternary discriminator function in universal algebra,Mathematische Annalen 191 (1971), 167–180.
Rosenblatt, D., On the graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices,Naval Res. Logist. Quarterly 4 (1957), 151–67.
Sapir, M. V., Problems of Burnside type and the finite basis property in varieties of semigroups, Math. USSR Izvestiya 30 (1988), 295–314.
Seneta, E.,Non-negative matrices, Halstead Press, John Wiley & Sons, New York, 1973.
Schwarz, Š., On the semigroup of binary relations on a finite set,Czechoslovakian Mathematics Journal 20 (1970), 632–679.
Schweigert, D., On varieties of clones,Semigroup Forum 18 (1979), 5–8.
— Clones of term functions of lattices and abelian groups,Algebra Universalis 20 (1985), 27–33.
— On algebras and clones,Semigroup Forum 35 (1987), 85–99.
Simel'gor, E. P., Identities in a finite symmetric semigroup,Modern Algebra (published by the Leningrad Pedagogical Institute) 1 (1974), 174–188. MR 55 #10583; Ref. Zh. 1974, 12A141.
Taylor, W., Characterizing Mal'tsev conditions,Algebra Universalis 3 (1973), 351–397.
— The fine spectrum of a variety,Algebra Universalis 5 (1975), 263–303.
— Mal'tsev conditions and spectra,Journal of the Australian Mathematical Society (A) 29 (1980), 143–152.
— Hyperidentities and hypervarieties,Aequationes Mathematicae 23 (1981), 30–49.
Walker, G., Fermat's Theorem for algebras,Pacific Journal of Mathematics 4 (1954), 317–320.
Wismath, S.,Hyperidentity and hypervariety results for varieties of semigroups, Ph. D. Thesis, Simon Fraser University, Burnaby, B. C., 1988.
Wismath, S., Hyperidentities for some varieties of semigroups,Algebra Universalis, to appear.
Wismath, S., Hyperidentities for some varieties of commutative semigroups,Algebra Universalis, to appear.
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Communicated by Norman R. Reilly
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Hyndman, J., McKenzie, R. & Taylor, W. k-ary monoids of term operations. Semigroup Forum 44, 21–52 (1992). https://doi.org/10.1007/BF02574322
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DOI: https://doi.org/10.1007/BF02574322