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Hagemann, Joachim; Herrmann, Christian

A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity. (English) Zbl 0419.08001

Arch. Math. 32, 234-245 (1979).
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Cited in 6 Reviews
Cited in 62 Documents

MSC:

08A30 Subalgebras, congruence relations
08B10 Congruence modularity, congruence distributivity
06C05 Modular lattices, Desarguesian lattices
06B10 Lattice ideals, congruence relations

Keywords:

commutators of congruences; algebras in congruence permutable varieties; centrality for congruence modular varieties; congruence lattice; dual ideal; semiprime congruences
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References:

[1] E. P. Armendariz andJ. W. Fischer, Regular P.I.-rings. Proc. Amer. Math. Soc.39, 247-251 (1973).
[2] G.Birkhoff, Lattice Theory. Providence R.I. 1967.
[3] P. M.Cohn, Universal algebra. New York 1965.
[4] R. Freese andB. J?nsson, Congruence modularity implies the Arguesian identity. Algebra Universalis6, 225-228 (1976). · Zbl 0354.08008 · doi:10.1007/BF02485830
[5] G. Gierz andK. Keimel, A lemma on primes appearing in algebra and analysis. Houston J. Math.3, 207-224 (1977). · Zbl 0359.06015
[6] J.Hagemann and C.Herrmann, Arithmetical locally equational classes and representation of partial functions. To appear in Coll. Math. Soc. J. Bolyai, Universal Algebra Conf. Esztergom 1977. · Zbl 0493.08005
[7] T. K. Hu, Locally equational classes of universal algebras. Chinese J. Math.1, 143-165 (1973). · Zbl 0371.08003
[8] B. J?nsson, Algebras whose congruence lattices are distributive. Math. Scand.21, 110-121 (1972). · Zbl 0167.28401
[9] K. Keimel, A unified theory of minimal prime ideals. Acta Math. Ac. Sci. Hung.32, 51-69 (1972). · Zbl 0265.06016 · doi:10.1007/BF01889903
[10] L. G. Kov?cs andM. F. Newman, Minimal verbal subgroups. Proc. Cambridge Phil. Soc.62, 347-350 (1966). · doi:10.1017/S0305004100039931
[11] R.McKenzie, Paraprimal varieties: a study of finite axiomatizability and definable principal congruences in locally finite varieties. To appear in Algebra Universalis. · Zbl 0383.08008
[12] F.Maeda, Kontinuierliche Geometrien. Berlin 1958.
[13] I. A. Mal’cev, On a general theory of algebraic systems (russian). Mat. Sbornik53, 3-20 (1954).
[14] I. A.Mal’cev, Algebraic Systems. Berlin 1973.
[15] J. D.H. Smith, Mal’cev varieties. Berlin 1976. · Zbl 0344.08002
[16] O. Steinfeld, Primelemente und Primradikale in gewissen verbandsgeordneten algebraischen Strukturen. Acta Math. Ac. Sci. Hung.19 243-261 (1968). · Zbl 0165.03002 · doi:10.1007/BF01894507
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