Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.2/3804
Título: The largest subsemilattices of the endomorphism monoid of an independence algebra
Autor: Araújo, João
Bentz, Wolfram
Konieczny, Janusz
Palavras-chave: Independence algebra
Semilattice
Monoid of endomorphisms
Dimension
Data: 2014
Citação: Araújo, João; Bentz, Wolfram; Konieczny, Janusz - The largest subsemilattices of the endomorphism monoid of an independence algebra. "Linear Algebra and its Applications" [Em linha]. ISSN 0024-3795. Vol. 458 (2014), p. 1-16
Resumo: An algebra A is said to be an independence algebra if it is a matroid algebra and every map α:X→A, defined on a basis X of A, can be extended to an endomorphism of A. These algebras are particularly well-behaved generalizations of vector spaces, and hence they naturally appear in several branches of mathematics such as model theory, group theory, and semigroup theory. It is well known that matroid algebras have a well-defined notion of dimension. Let A be any independence algebra of finite dimension n , with at least two elements. Denote by End(A) the monoid of endomorphisms of A. We prove that a largest subsemilattice of End(A) has either 2n−1 elements (if the clone of A does not contain any constant operations) or 2n elements (if the clone of A contains constant operations). As corollaries, we obtain formulas for the size of the largest subsemilattices of: some variants of the monoid of linear operators of a finite-dimensional vector space, the monoid of full transformations on a finite set X, the monoid of partial transformations on X, the monoid of endomorphisms of a free G-set with a finite set of free generators, among others. The paper ends with a relatively large number of problems that might attract attention of experts in linear algebra, ring theory, extremal combinatorics, group theory, semigroup theory, universal algebraic geometry, and universal algebra.
Peer review: yes
URI: http://hdl.handle.net/10400.2/3804
DOI: 10.1016/j.laa.2014.05.041
ISSN: 0024-3795
Versão do Editor: http://www.sciencedirect.com/science/article/pii/S0024379514003619
Aparece nas colecções:Matemática e Estatística - Artigos em revistas internacionais / Papers in international journals

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