Independence algebras, basis algebras and the distributivity condition

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorBentz, Wolfram-
Autor(es): dc.creatorGould, Victoria-
Data de aceite: dc.date.accessioned2025-08-22T11:47:49Z-
Data de disponibilização: dc.date.available2025-08-22T11:47:49Z-
Data de envio: dc.date.issued2023-01-29-
Data de envio: dc.date.issued2023-01-29-
Data de envio: dc.date.issued2020-10-21-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/13253-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/13253-
Descrição: dc.descriptionPreprint de "W. Bentz and V. Gould, “Independence Algebras, Basis Algebras and the Distributivity Condition”, Acta Mathematica Hungarica 162 (2020), 419–444."-
Descrição: dc.descriptionStable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that of independence algebras, and reflecting the way in which free modules over well-behaved domains generalise vector spaces. If a stable basis algebra B satisfies the distributivity condition (a condition satisfied by all the previously known examples), it is a reduct of an independence algebra A. Our first aim is to give an example of an independence algebra not satisfying the distributivity condition. Gould showed that if a stable basis algebra B with the distributivity condition has finite rank, then so does the independence algebra A of which it is a reduct, and that in this case the endomorphism monoid End(B) of B is a left order in the endomorphism monoid End(A) of A. We complete the picture by determining when End(B) is a right, and hence a two-sided, order in End(A). In fact (for rank at least 2), this happens precisely when every element of End(A) can be written as α]β where α, β ∈ End(B), α] is the inverse of α in a subgroup of End(A) and α and β have the same kernel. This is equivalent to End(B) being a special kind of left order in End(A) known as straight.-
Descrição: dc.descriptioninfo:eu-repo/semantics/publishedVersion-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Publicador: dc.publisherSpringer-
Direitos: dc.rightshttp://creativecommons.org/licenses/by/4.0/-
Palavras-chave: dc.subjectIndependence algebras-
Palavras-chave: dc.subjectBasis algebras-
Palavras-chave: dc.subjectV∗-algebras-
Palavras-chave: dc.subjectReduct-
Palavras-chave: dc.subjectOrder-
Título: dc.titleIndependence algebras, basis algebras and the distributivity condition-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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