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Complements in lattices of varieties and equational theories (1994)

Diercks, V. ; Erné, M. ; Reinhold, J.

Springer

Algebra universalis 31 (1994), S. 506-515

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ISSN: 1420-8911

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We investigate various weak conditions ensuring that a lattice be complemented. Using these general results in connection with a famous result due to Lampe, we show that the lattice of all equational theories containing a fixed theory must be complemented if it is lower semicomplemented, thereby answering in the affirmative a question raised by Volkov and Vernikov. Moreover, such a lattice must be a finite Boolean algebra if it has one of the following properties: upper or lower sectionally complemented; incomparably complemented; lower semicomplemented and lower semimodular; or atomistic and upper semimodular.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01236502

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