References
J. AczélProof of a theorem on distributive type hyperidentities, Algebra Universalis1 (1971), 1–7.
A. A. Akataev and D. M. Smirnov,The lattice of submanifolds of an algebraic manifold (in Russian), Algebra i Logika7, (1968), 5–25; English translation: Algebra and Logic7 (1968), 3–13.
A. K. Austin,A note on models of identities, Proc. Amer. Math. Soc.16 (1965), 522–523.
A. K. Austin,Finite models for laws in two variables, Proc. Amer. Math. Soc.17 (1966), 1410–1412.
J. L. Bell and A. B. Slomson,Models and ultraproducts: an, introduction, North-Holland, Amsterdam, 1969.
G. Birkhoff,On the structure of abstract algebras, Proc. Cambridge Philos. Soc.31 (1935), 433–454.
G. Birkhoff,Lattice theory (3rd edition), Amer. Math. Soc. Colloq. Publ. #25, Providence, 1967.
G. Birkhoff, and O. Frink,Representation of lattices by sets. Trans. Amer. Math. Soc.64 (1948), 299–316.
G. Birkhoff and J. D. Lipson,Heterogeneous algebras, J. Combinatorial Theory8 (1970), 115–133.
S. Burris,Models in equational theories of unary algebras, Algebra Universalis1 (1972), 386–392.
A. Church,Introduction to mathematical logic I, Princeton University Press, Princeton, 1956.
P. M. Cohn,Universal algebra, Harper and Row, New York, 1965.
B. Csákány,On the equivalence of certain classes of algebraic systems (in Russian), Acta Sci. Math. (Szeged)23 (1962), 46–57.
B. Csákány,Primitive classes of algebras which are equivalent to classes of semi-modules and modules (in Russian) Acta Sci. Math. (Szeged)24 (1963), 157–164.
B. Csákány,Abelian properties of primitive classes of universal algebras (in Russian), Acta Sci. Math. (Szeged)25, (1964), 202–208.
B. Csákány,Characterization of regular varieties, Acta Sci. Math. (Szeged)31 (1970), 187–189.
A. Day,A characterization of modularity for congruence lattices of algebras, Canad. Math. Bull.12 (1969), 167–173.
A. Day,A note on the congruence extension property, Algebra Universalis1 (1971), 234–235.
T. Evans,Properties of algebras almost equivalent to, identities, J. London Math. Soc.37 (1962), 53–59.
T. Evans,The spectrum of a variety, Z. Math. Logik Grundlagen Math.,13 (1967), 213–218.
S. Fajtlowicz,Birkhoff’s theorem in the category of non-indexed algebras, Bull. Acad. Pol. Sci., Sér. sci. math. astr. et phys.17 (1969), 273–275.
S. Fajtlowicz,Algebras of homomorphisms, Rend. Math. (6)3 (1970), 523–527.
S. Fajtlowicz, W. Holsztyński, J. Mycielski, and B. Weglorz,On powers of bases in some compact algebras, Colloq. Math.19 (1968), 43–46.
W. Felscher, Equational maps, 121–161 in H. A. Schmidt, K. Schütte and H.-J. Thiele (eds.)Contributions to mathematical logic, North-Holland, Amsterdam, 1968.
K. Fichtner,Varieties of universal algebras with ideals (in Russian), Mat. Sbornik,75 (117) (1968), 445–453; English translation: Math. USSR-Sbornik4 (1968), 411–418.
K. Fichtner,Distributivity and modularity in varieties of algebras, Acta Sci. Math. (Szeged)33 (1972), 343–348.
G. A. Fraser and A. Horn,Congruence relations in direct products, Proc. Amer. Math. Soc.26 (1970), 390–394.
P. Freyd,Abelian categories, Harper and Row, New York, 1964.
N. Funayama and T. Nakayama,On the distributivity of a lattice of lattice-congruences, Proc. Imp. Acad. Tokyo18 (1942), 553–554.
A. Goetz,On weak isomorphisms and weak homomorphisms of abstract algebras, Colloq. Math.14 (1966), 163–167.
A. Goetz,A generalization of the notion of direct product of universal algebras, Colloq. Math.22 (1971), 167–176.
A. Goetz and C. Ryll-Nardzewski,On bases of abstract algebras, Bull. Acad. Pol. Sci., Sér. sci. math., astr. et phys.8 1960), 157–161.
G. Grätzer,On spectra of classes of universal algebras, Proc. Amer. Math. Soc.18 (1967), 729–735.
G. Grätzer,Universal algebra, van Nostrand, Princeton, 1968.
G. Grätzer,Two Mal’cev-type theorems in universal algebra, J. Combinatorial theory8 (1970), 334–342.
G. Grätzer, H. Lakser, and J. Płonka,Joins and direct products of equational classes, Canad. Math. Bull.12 (1969), 741–744.
J. Hagemann,On regular and weakly regular congruences, Algebra Universalis (to appear).
J. Hagemann and A. Mitschke,On n-permutable congruences Algebra Universalis (to appear).
L. Henkin, J. D. Monk, and A. Tarski,Cylindric algebras, North-Holland, Amsterdam, 1971.
P. J. HigginsAlgebras with a scheme of operators, Math. Nachr.27 (1963), 115–132.
D. Hilbert,The foundations of geometry, translated by E. J. Townsend, Open Court, Chicago, 1902, 1910.
T.-K. Hu,On equational classes of algebras in which congruences of finite direct products are induced by congruences on their factors, mimeographed, Southern Illinois University (1968?).
T.-K. Hu,Stone duality for primal algebra theory, Math. Z.110 (1969), 180–198.
T.-K. Hu,Direct factorization in certain classes of universal algebras, Abstract 672–304, Notices Amer. Math. Soc.17 (1970), 169.
T.-K. Hu,On the topological duality for primal algebra theory, Algebra Universalis1 (1971), 152–154.
T.-K. Hu and P. Kelenson,Independence and direct factorization of universal algebras, Math. Nachr.51 (1971), 83–99.
B. Jónsson,Algebras whose congruence lattices are distributive, Math. Scand.21 (1967), 110–121.
L. Kalmár,Contributions to the reduction theory of the decision problem, Fourth paper:Reduction to a finite set of individuals Acta Math. Acad. Sci. Hung.2 (1951), 125–142.
D. KellyBasic equations: word problems and Mal’cev conditions, Abstract 701-08-4, Notices Amer. Math. Soc.20 (1973), A-54.
G. Kreisel and J. L. Krivine,Elements of mathematical logic (model theory), North-Holland, Amsterdam, 1967.
J.-L. Lagrange,Réflexions sur la résolution algébrique des équations, Nouveaux Mémoires de I’Académie Royale des Sciences et Belles Lettres de Berlin, 1770–1771.
F. W. Lawvere,Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci.50 (1963), 869–872.
F. W. Lawvere,Some algebraic problems in the context of functorial semantics of algebraic theories, pp. 51–61 in Lecture Notes in Mathematics61 Springer-Verlag, Berlin, 1968.
F. E. J. Linton,Some aspects of equational, categories, pp. 84–89 in: S. Eilenberg, D. K. Harrison, S. MacLane and H. Röhrl, eds.. Proceedings of the conference on categorical algebra, La Jolla, 1965. Springer-Verlag, Berlin and New York, 1966.
J. Łoś,Direct sums in general algebra, Colloq. Math.14 (1966), 33–38.
S., MacLane,Categorical algebra, Bull. Amer. Math. Soc.71 (1965), 40–106.
A. I. Mal’cev,On the general theory of algebraic systems (in Russian). Math. Sbornik (N. S.)35 (77) (1954), 3–20. English translation: Amer. Math Soc. Translations (2)27 (1963), 125–142.
A. I. Mal’cev,The structural characterization of certain classes of algebras (in Russian), Dokl. Akad. Nauk S.S.S.R.120 (1958), 29–32. English translation: Chapter 9 of [60].
A. I. Mal’cev,Model correspondences, Izv. Akad. Nauk S.S.R. Ser. Mat.23 (1959), 313–316. English translation: Chapter 11 of [60].
A. I. Mal’cev,The metamathematics of algebraic systems, collected papers 1936–67, translated and edited by B.F. Wells III, North-Holland, Amsterdam, 1971.
E. Marczewski,Independence in abstract algebras-results and problems Colloq. Math.14 (1966), 169–188.
G. F. McNulty,The decision problem for equational bases of algebras, Ph.D. Thesis, University of California, Berkeley, 1972.
A. Mitschke,Implication algebras are 3-permutable and 3-distributive, Algebra Universalis1 (1971), 182–186.
J. B. Nation,Varieties whose congruences satisfy certain lattice identities, Algebra Universalis (to appear).
B. H. Neumann,On a problem of G. Grätzer, Publ. Math. Debrecen.,14 (1967), 325–329.
B. H. Neumann and E. C. Wiegold,A semigroup representation of varieties of algebras, Colloq. Math.14 (1966), 111–114.
W. D. Neumann,Representing varieties of algebras by algebras, J. Austral. Math. Soc.11 (1970), 1–8.
R. Padmanabhan,Characterization of a class of groupoids, Algebra Universalis1 (1972), 374–382.
B. Pareigis,Categories and functors, Academic Press, New York, 1970.
P. Perkins,Unsolvable problems for equational theories, Notre Dame J. Formal Logic3 (1967), 175–185.
D. Pigozzi,Amalgamation, congruence-extension and interpolation properties in algebras, Algebra Universalis1 (1972), 269–349.
A. F. Pixley,Distributivity and permutability of congruence relations in equational classes of algebras, Proc. Amer. Math. Soc.14 (1963), 105–109.
A. F. Pixley,Local Mal’cev conditions, Canad. Math. Bull.15 (1972), 559–568.
R. W. Quackenbush,Demi-semi-primal algebras and Mal’cev-type conditions, Math. Z.122 (1971), 166–176.
R. W. Quackenbush,Models for Mal’cev conditions: n-permutability, Abstract 71T-A182, Notices Amer. Math. Soc.18 (1971), 806.
P. C. Rosenbloom,Post algebras. I. Postulates and general theory, Amer. J. Math.64 (1942), 167–188.
R. Roth,El origen de la teoría de grupos. El teorema de Lagrange (1771), Bol. Math.,3 (1969), 137–141.
D. Sachs,Identities in finite partition lattices, Proc. Amer. Math. Soc.12 (1969), 944–945.
B. M. Schein,A remark on bisimple inverse semigroups, Semigroup Forum3 (1971), 80–83.
A. Schmidt,Über deduktive Theorien mit mehreren Sorten von Grunddingen, Math. Ann.115 (1938), 485–506
A. Schmidt,Die Zulässigkeit der Behandlung mehrsortiger Theorien mittels der üblichen einsortigen Prädikatenlogik, Math. Ann.123 (1951), 187–200.
E. T. Schmidt,Kongruenzrelationen algebraischer Strukturen, Math. Forschungsberichte25, Berlin, 1969.
E. T. Schmidt,Über reguläre Mannigfaltigkeiten, Acta Sci. Math. (Szeged)31 (1970), (197–201.
E. T. Schmidt,On n-permutable equational classes, Acta Sci. Math. (Szeged) 33 (1972), 29–30.
J. Słomiński,On the determining of the form of congruences in abstract algebras with equationally definable constant elements, Fund. Math.48 (1960), 325–341.
S. K. Stein,Finite models of identities, Proc. Amer. Math. Soc.14 (1963), 216–222.
M. G. Stone,Proper congruences do not imply a modular congruence lattice, Colloq. Math.23 (1971), 25–27.
S. Świerczkowski,On ismorphic free algebras, Fund. Math. 50 (1961) 35–44.
A. Tarski,Equational logic and equational theories of algebras, p. 275–288, in: H.A. Schmidt, K. Schütte, and H.-J. Thiele (eds.), Contributions to mathematical logic, North-Holland, Amsterdam, 1968.
W. Taylor,Some constructions of compact algebras, Ann. Math. Logic3 (1971), 395–435.
W. Taylor,Fixed points of endomorphisms, Algebra Universalis2 (1972), 74–76.
W. Taylor,Characterizing Mal’cev conditions, Abstract 72T-A98, Notices Amer. Math. Soc.19 (1972), A431.
W. Taylor,Varieties without doubleton algebras, Abstract 72T-A280, Notices Amer. Math. Soc.19 (1972), A-753.
H. A. Thurston,Derived operations and congruences, Proc. London Math. Soc. (3)8 (1958), 127–134.
B. A. TrakhtenbrotThe impossibility of an algorithm for the problem of satisfiability in finite classes, Dokl. Akad. Nauk S.S.S.R. (N.S.)70 (1950), 569–572.
I. I. Valutse,Universal algebras with regular but not permutable congruences (in Russian), Uspekh. Mat. Nauk18 (3) (1963), 145–148.
L. I. Wade,Post algebras and rings, Duke Math. J.12 (1945), 389–395.
H. Wang,Logic of many-sorted theories, J. Symbolic Logic,17 (1952), 105–116.
R. Wille,Kongruenzklassengeometrien, Lecture notes in mathematics #113, Springer-Verlag, Berlin, 1970.
G. C. Wraith,Algebraic theories, Aarhus University Lecture Notes Series No. 22, April, 1970.
G. C. Wraith,Algebras over theories, Colloq. Math.23 (1971), 181–190.
Additional references
J. Adámek and J. Reiterman,Fixed-point property of unary algebras, Algebra Universalis (to appear).
O. Chein,Lagrange’s Theorem for M k-loops, Arch. Math. (Basel)24 (1973), 121–122.
A. Day,p-Modularity implies modularity in equational classes, Algebra Universalis (to appear).
E. Gedeonová,Acta F.R.N. Univ., Commen. Math.28 (1972), 99–106.
L. Klukovits,Hamiltonian varieties of universal algebras, Acta Sci. Math. (Szeged) (to appear).
R. McKenzie,Simple undecidable problems about finite groupoids (preliminary report), Abstract 73T-E95, Notices Amer. Math. Soc.20 (1973), A-505.
A. Shafaat,Lattices of subsemivarieties of certain varieties, J. Austral. Math. Soc.,12 (1971), 15–20.
A. Ursini,Sulle varietà di algebre con una buona teoria degli ideali, Boll. Unione Mat. Ital. (4)6 (1972), 90–95.
A. Ursini,Osservazioni sulle varietà BIT, Boll. Unione Mat. Ita. (4)7 (1973), 205–211.
S. Bulman-Fleming, A. Day and W. Taylor,Regularity and modularity of congruences, Algebra Universalis (to appear).
R. A. Dean,Component subsets of the free lattice on n generators, Proc. Amer. Math. Soc.7 (1956), 220–226.
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Supported by NSF grants GP-19405A and GP-34744X.
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Taylor, W. Characterizing Mal’cev conditions. Algebra Univ. 3, 351–397 (1973). https://doi.org/10.1007/BF02945141
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DOI: https://doi.org/10.1007/BF02945141