Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T16:03:56.286Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of Varieties with a Difference Term

Published online by Cambridge University Press:  20 November 2018

Paolo Lipparini
Paolo Lipparini*
Affiliation:
Dipartimento di matematica, Università di Cagliari
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.

We characterize, by means of congruence identities, all varieties having a weak difference term, and all neutral varieties. Our characterization of varieties with a difference term is new even in the particular case of locally finite varieties.

Keywords

08B0508B99Variety with a (weak) difference termcommutatorneutral variety
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 308 - 315
Copyright
Copyright © Canadian Mathematical Society 1996

References

[BS] Burris, S., Sankappanavar, H. P., A course in universal algebra, New York, 1981.Google Scholar
[DG] Day, A., Gumm, H. P., Some characterizations of the commutator, Algebra Universalis, 29(1992), 61–78.Google Scholar
[FMKj Freese, R., McKenzie, R., Commutator theory for congruence modular varieties, London Math. Soc. Lecture Notes, 125(1987).Google Scholar
[Gu] Gumm, H. P., Geometrical methods in congruence modular algebras, Amer. Math. Soc. Memoirs, 286 (1983).Google Scholar
[HH] Hagemann, J. and Herrmann, C., A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity, Arch. Math. (Basel), 32(1979), 234–245.Google Scholar
[HM] Hagemann, J. and Mitschke, A., On n-permutable congruences, Algebra Universalis, 3(1973), 11–12.Google Scholar
[HMK] Hobby, D. and McKenzie, R., The structure of finite algebras, Contemp. Math. 76(1988).Google Scholar
[Kel] Kearnes, K. A., An Order-theoretic Property of the Commutator, Internat. J. Algebra Comput., 3(1993), 491–533.Google Scholar
[Ke2] Kearnes, K. A., Varieties with a difference term, preprint.Google Scholar
[KMK] Kearnes, K. and McKenzie, R., Commutator theory for relatively modular quasivarieties, Trans. Amer. Math. Soc, 331(1992), 465–502.Google Scholar
[Ki] Kiss, E. W., Three remarks on the modular commutator. Algebra Universalis. 29( 1992), 455–476.Google Scholar
[KPJ Kiss, E. W. and P., Prôhle, Problems and results in tame congruence theory. A survey of the ‘88 Budapest Workshop, Algebra Universalis, 29(1992), 151–171.Google Scholar
[KQ] Kiss, E. W. and Quackenbush, R., General Commutator Theory via Linear Algebra, Notes.Google Scholar
[Lpl] Lipparini, P., n-permutable varieties satisfy nontrival congruence identities, Algebra Universalis, 33 (1995), 159–168.Google Scholar
[Lp2] Lipparini, P., Commutator Theory without join-distrihutivity, Trans. Amer. Math. Soc. 346(1994), 177–202.Google Scholar
[Lp3] Lipparini, P., Varieties satisfying some forms of Herrmann s theorem, in preparation.Google Scholar
[Lp4] Lipparini, P., Difference terms and the cyclic commutator, in preparation.Google Scholar
[Lp5] Lipparini, P., Congruence identities satisfied in n-permutable varieties, Bollettino Unione Matematica Italiana, Ser. VII, 8-B(1994), 851–868.Google Scholar
[MKNT] McKenzie, R., McNulty, G. and Taylor, W., Algebras, Lattices, Varieties, 1, Monterey, 1987.Google Scholar
[Qu] Quackenbush, R., Quasi-affine algebras, Algebra Universalis, 20(1985), 318–327.Google Scholar
[Sm] Smith, J. D. H., Mai'cev varieties, LNM, 554(1976).Google Scholar
[Ta] Taylor, W., Some applications of the Term Condition, Algebra Universalis, 14(1982), 11—24.Google Scholar