Taylor, Walter Hyperidentities and hypervarieties. (English) Zbl 0491.08009 Aequationes Math. 23, 30-49 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 ReviewsCited in 45 Documents MSC: 08B05 Equational logic, Mal’tsev conditions 16Rxx Rings with polynomial identity 20M05 Free semigroups, generators and relations, word problems 20E10 Quasivarieties and varieties of groups Keywords:hypervariety; product varieties; subvarieties; reduct varieties; hyperidentity; variety of lattices; variety of commutative rings Citations:Zbl 0387.08004 PDF BibTeX XML Cite \textit{W. Taylor}, Aequationes Math. 23, 30--49 (1981; Zbl 0491.08009) Full Text: DOI EuDML OpenURL References: [1] Aczél, J. (1971)Proof of a theorem on distributive type hyperidentities. Algebra Universalis1, 1–6. · Zbl 0219.08008 [2] Baker, K. (1969)Equational classes of modular lattices. Pacific J. Math.28, 9–15. · Zbl 0174.29802 [3] Belousov, V. D. (1965)Systems of quasigroups with generalized identities. Uspekhi Mat. Nauk20 (121), 75–146. English Translation: Russian Math. Surveys20, 75–143. · Zbl 0135.03503 [4] Bergman, G. M. (1981)Hyperidentities of groups and semigroups. Aequationes Math.23, 50–65. · Zbl 0485.08005 [5] Birkhoff, G. (1935)On the structure of abstract algebras. Proc. Cambridge Philos. Soc.31, 433–454. · JFM 61.1026.07 [6] Cohn, P. M. (1965)Universal Algebra, Harper and Row, New York. [7] Evans, T. (1962)Endomorphisms of abstract algebras. Proc. Roy Soc. Edinburgh Sect. A66, 53–64. · Zbl 0135.02503 [8] (1967)Products of points – some simple algebras and their identities. Amer. Math. Monthly74, 362–372. · Zbl 0207.32901 [9] Fajtlowicz, S. (1969)Birkhoff’s theorem in the category of non-indexed algebras. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.17, 273–275. · Zbl 0179.03602 [10] Grätzer, G. (1968)Universal Algebra. Van Nostrand, Princeton. [11] (1970)Composition of functions. Queen’s Papers in Pure and Applied Math, vol. 25. [12] (1979)Universal Algebra. Springer-Verlag. · Zbl 0412.08001 [13] Higgins, P. J. (1963)Algebras with a scheme of operators. Math. Nachr.27, 115–132. · Zbl 0117.25903 [14] Lausch, H. andNöbauer, W. (1973)Algebra of Polynomials. North-Holland, Amsterdam. · Zbl 0283.12101 [15] McKenzie, R. (1970)Equational bases for lattice theories. Math. Scand.27, 24–38. · Zbl 0307.08001 [16] Neumann, W. D. (1978)Mal’cev conditions, spectra and Kronecker product. J. Austral. Math. Soc. (A)25, 103–117. · Zbl 0387.08004 [17] Pigozzi, D. (1980)Universal equational theories and varieties of algebras. Ann. Mat. Logic17 (1979), 117–150. · Zbl 0436.03021 [18] Quackenbush, R. W. (1979)Primality, etc. – Appendix to Grätzer (1979). [19] Taylor, W. (1973)Characterizing Mal’cev conditions. Algebra Universalis3, 351–397. · Zbl 0304.08003 [20] (1975)The fine spectrum of a variety, Algebra Universalis5, 263–303. · Zbl 0336.08004 [21] Taylor, W. (1979)Hyperidentities and hypervarieties. Abstract 79T-A34, Notices Amer. Math. Soc.26, A-240. [22] (1980)Equational logic (survey). Houston J. Math.,5 (1979), 1–83. [23] (1981)Mal’tsev conditions and spectra. J. Austral. Math. Soc. (A)29, 143–152. · Zbl 0439.08005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.