Maria de Lurdes Azevedo Teixeira

@uminho.pt

Departamento de Matemática - Escola de Ciências da Universidade do Minho
Universidade do Minho

Maria de Lurdes Azevedo Teixeira


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https://researchid.co/mlurdesteixeira

RESEARCH INTERESTS

Álgebra. Finite Semigroup Theory
11

Scopus Publications

Scopus Publications

  • Asymptotic behavior of the overlap gap between infinite words
    J. C. Costa, C. Nogueira, M. L. Teixeira
    Semigroup Forum, 2024
    We proceed with the study of ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word $$\\lambda $$ λ and the prefixes of a right-infinite word $$\\rho $$ ρ . For a positive integer n, let g(n) be n minus the maximum length of overlaps between the suffix of $$\\lambda $$ λ and the prefix of $$\\rho $$ ρ of length n. In a recent publication we have shown that the function g has finite image if and only if $$\\lambda $$ λ and $$\\rho $$ ρ are ultimately periodic words with a same root. In this paper we give an asymptotic characterization of words $$\\lambda $$ λ and $$\\rho $$ ρ for which the function g has finite image. We prove that this condition is true if and only if the sequence $$\\big (g(n)/n\\big )_n$$ ( g ( n ) / n ) n tends to zero
  • The Overlap Gap between Left-Infinite and Right-Infinite Words
    José Carlos Costa, Conceição Nogueira, Maria Lurdes Teixeira
    International Journal of Foundations of Computer Science, 2022
    We study ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word [Formula: see text] and the prefixes of a right-infinite word [Formula: see text]. The main theorem states that the set of minimum lengths of words [Formula: see text] and [Formula: see text] such that [Formula: see text] or [Formula: see text] is finite, where [Formula: see text] runs over positive integers and [Formula: see text] and [Formula: see text] are respectively the suffix of [Formula: see text] and the prefix of [Formula: see text] of length [Formula: see text], if and only if [Formula: see text] and [Formula: see text] are ultimately periodic words of the form [Formula: see text] and [Formula: see text] for some finite words [Formula: see text], [Formula: see text] and [Formula: see text].
  • The word problem for κ -terms over the pseudovariety of local groups
    J. C. Costa, C. Nogueira, M. L. Teixeira
    Semigroup Forum, 2021
    In this paper we study the $\\kappa$-word problem for the pseudovariety ${\\bf LG}$ of local groups, where $\\kappa$ is the canonical signature consisting of the multiplication and the pseudoinversion. We solve this problem by transforming each arbitrary $\\kappa$-term $\\alpha$ into another one called the canonical form of $\\alpha$ and by showing that different canonical forms have different interpretations over ${\\bf LG}$. The procedure of construction of these canonical forms consists in applying elementary changes determined by a certain set $\\Sigma$ of $\\kappa$-identities. As a consequence, $\\Sigma$ is a basis of $\\kappa$-identities for the $\\kappa$-variety generated by ${\\bf LG}$.
  • On κ-reducibility of pseudovarieties of the form v ∗ D
    J. C. Costa, M. L. Teixeira, C. Nogueira
    International Journal of Algebra and Computation, 2017
    This paper deals with the reducibility property of semidirect products of the form [Formula: see text] relatively to graph equation systems, where D denotes the pseudovariety of definite semigroups. We show that if the pseudovariety [Formula: see text] is reducible with respect to the canonical signature [Formula: see text] consisting of the multiplication and the [Formula: see text]-power, then [Formula: see text] is also reducible with respect to [Formula: see text].
  • Pointlike reducibility of pseudovarieties of the form v ∗ D
    José Carlos Costa, Conceição Nogueira, Maria Lurdes Teixeira
    International Journal of Algebra and Computation, 2016
    In this paper, we investigate the reducibility property of semidirect products of the form [Formula: see text] relatively to (pointlike) systems of equations of the form [Formula: see text], where [Formula: see text] d̃enotes the pseudovariety of definite semigroups. We establish a connection between pointlike reducibility of [Formula: see text] and the pointlike reducibility of the pseudovariety [Formula: see text]. In particular, for the canonical signature [Formula: see text] consisting of the multiplication and the [Formula: see text]-power, we show that [Formula: see text] is pointlike [Formula: see text]-reducible when [Formula: see text] is pointlike [Formula: see text]-reducible.
  • Semigroup presentations for test local groups
    J. C. Costa, C. Nogueira, M. L. Teixeira
    Semigroup Forum, 2015
    In this paper we exhibit a type of semigroup presentation which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety $$\\mathbf{LG}$$LG of all finite local groups and use them as test-semigroups to prove that $$\\mathbf{LG}$$LG and $$\\mathbf{S}$$S, the pseudovariety of all finite semigroups, verify the same $$\\kappa $$κ-identities involving $$\\kappa $$κ-terms of rank at most 1, where $$\\kappa $$κ denotes the implicit signature consisting of the multiplication and the $$(\\omega -1)$$(ω-1)-power.
  • Semidirect product with an order-computable pseudovariety and tameness
    J. Almeida, J. C. Costa, M. L. Teixeira
    Semigroup Forum, 2010
    The semidirect product of pseudovarieties of semigroups with an order-computable pseudovariety is investigated. The essential tool is the natural representation of the corresponding relatively free profinite semigroups and how it transforms implicit signatures. Several results concerning the behavior of the operation with respect to various kinds of tameness properties are obtained as applications.
  • Tameness of the pseudovariety LS1
    J. C. COSTA, M. L. TEIXEIRA
    International Journal of Algebra and Computation, 2004
    The notion of κ-tameness of a pseudovariety was introduced by Almeida and Steinberg and is a strong property which implies decidability of pseudovarieties. In this paper we prove that the pseudovariety LSl, of local semilattices, is κ-tame.
  • The Semidirectly Closed Pseudovariety Generated by Aperiodic Brandt Semigroups
    M. LURDES TEIXEIRA
    International Journal of Algebra and Computation, 2001
    This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B2, denoted V*(B2). We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by B2 which leads to the main result, which states that V*(B2) is decidable. Independently, using some suggestions given by J. Almeida in his book "Finite Semigroups and Universal Algebra", we constructed an algorithm to solve the membership problem in V* (B2).
  • On semidirectly closed pseudovarieties of aperiodic semigroups
    M.Lurdes Teixeira
    Journal of Pure and Applied Algebra, 2001
    The aim of this work is to study the unknown intervals of the lattice of aperiodic pseudovarieties which are semidirectly closed and answer questions proposed by Almeida in his book “Finite Semigroups and Universal Algebra”. The main results state that the intervals [ V ∗ (B 2 ), ER ∩ LR ] and [ V ∗ (B 2 1 ), ER ∩ A ] are not trivial, and that both contain a chain isomorphic to the chain of real numbers. These results are a consequence of the study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B 2 .
  • On finitely based pseudovarieties of the forms V * D and V * Dn1
    Jorge Almeida, Assis Azevedo, Lurdes Teixeira
    Journal of Pure and Applied Algebra, 2000