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Ideals and other generalizations of congruence classes

Part of: Algebraic structures Varieties

Published online by Cambridge University Press:  09 April 2009

Paolo Agliano  and
Aldo Ursini
Paolo Agliano
Affiliation:
Dipartimento di MatematicaUniversitá di SienaVia del Capitano 53100 Siena, Italy
Aldo Ursini
Affiliation:
Dipartimento di MatematicaUniversitá di SienaVia del Capitano 53100 Siena, Italy
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Abstract

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In the general context of ideals in universal algebras, we study varietal properties connected with ideals that are equivalent both to Ma'cev conditions and congruence properties such as 0-regularity, 0-permutability, etc.

MSC classification

Secondary: 08A30: Subalgebras, congruence relations 08B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 1 , August 1992 , pp. 103 - 115
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Agliano, P., ‘The prime spectrum of a universal algebra’, Rivista di Mat. Pura ed Appl., 4 (1989), 83–91.Google Scholar
[2]Agliano, P. and Ursini, A., ‘Cosets in universal algebra’, J. of Algebra, 107 (1987), 376–384.Google Scholar
[3]Agliano, P. and Ursini, A., ‘On some ideal basis theorems’, Rapporto Matematico n. 182, Universitá di Siena (1988).Google Scholar
[4]Fichtner, K., ‘Eine bemerkung über mannigfaltigkeiten universeller algebren mit idealen’, Monatsch. d. Deutsch. Akad. d. Wissen (Berlin) 12 (1970), 21–45.Google Scholar
[5]Gumm, H.P. and Ursini, A., ‘Ideals in Universal Algebra’, Algebra Universalis 19 (1984), 45–54.CrossRefGoogle Scholar
[6]Maĺcev, A.I., ‘On the general theory of algebraic systems’, Mat. Sborsnik 77 (1954), 3–20.Google Scholar
[7]McKenzie, R., McNulty, G. and Taylor, W., Algebras, lattices, varietie, Volume I, Wadsworth and Brooks Cole, Monterey, California, 1987.Google Scholar
[8]Mitschke, A., ‘Implication algebras are 3-permutable and 3-distributive’, Algebra Universalis 1 (1971), 182–186.CrossRefGoogle Scholar
[9]Ursini, A., ‘Sulle varietá di algebre con una buona teoria degli ideali’, Boll. U.M.I. 6 (1972), 90–95.Google Scholar
[10]Ursini, A., ‘Osservazioni sulla varietá BIT’, Boll, U.M.I. 8 (1973), 205–211.Google Scholar
[11]Ursini, A., ‘Ideals and their Calculus I’, Rapporto Matematico n.41, Universitá di Siena, (1981).Google Scholar
[12]Werner, H., ‘A Maĺcev condition for admissible relations’, Algebra Universalis 3 (1973), 263.Google Scholar