Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-14T06:46:12.716Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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