Publications

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A
André, J. M., V. H. Fernandes, and J. D. Mitchell. "Largest 2-generated subsemigroups of the symmetric inverse semigroup." Proc. Edinb. Math. Soc. (2). 50 (2007): 551-561.Website
Araújo, Isabel M., Mário J. J. Branco, Vitor H. Fernandes, Gracinda M. S. Gomes, and N. Ruškuc. "On generators and relations for unions of semigroups." Semigroup Forum. 63 (2001): 49-62.
Araújo, João, Vítor H. Fernandes, Manuel M. Jesus, Victor Maltcev, and James D. Mitchell. "Automorphisms of partial endomorphism semigroups." Publicationes Mathematicae Debrecen. 79.1-2 (2011): 23-39.
C
Caneco, Rita, Vítor H. Fernandes, and Teresa M. Quinteiro. "Ranks and presentations of some normally ordered inverse semigroups." (Submitted). AbstractWebsite

In this paper we compute the rank and exhibit a presentation for the monoids
of all $P$-stable and $P$-order preserving partial permutations on a finite set
$\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)
semigroups constitute a natural class of generators of the pseudovariety of
inverse semigroups ${\sf NO}$ of all normally ordered (finite) inverse
semigroups.

Cicalò, Serena, Vítor H. Fernandes, and Csaba Schneider. "Partial transformation monoids preserving a uniform partition." Semigroup Forum (DOI 10.1007/s00233-014-9629-5). 90.2 (2015): 532-544. AbstractWebsite

The objective of this paper is to study the monoid of all partial
transformations of a finite set that preserve a uniform partition. In addition
to proving that this monoid is a quotient of a wreath product with respect to a
congruence relation, we show that it is generated by 5 generators, we compute
its order and determine a presentation on a minimal generating set.

Cordeiro, E., M. Delgado, and V. H. Fernandes. "Relative abelian kernels of some classes of transformation monoids." Bull. Austral. Math. Soc.. 73 (2006): 375-404.Website
D
Delgado, Manuel, and Vítor H. Fernandes. "Rees quotients of numerical semigroups." Portugaliae Mathematica. 70.2 (2013): 93-112. AbstractWebsite

We introduce a class of finite semigroups obtained by considering Rees
quotients of numerical semigroups.
Several natural questions concerning this class, as well as particular
subclasses obtained by considering some special ideals, are answered while
others remain open. We exhibit nice presentations for these semigroups and
prove that the Rees quotients by ideals of N, the positive integers under
addition, constitute a set of generators for the pseudovariety of commutative
and nilpotent semigroups.

Delgado, Manuel, and Vítor H. Fernandes. "Solvable monoids with commuting idempotents." Int. J. Algebra Comput.. 15 (2005): 547-570. Abstract

The notion of the Abelian kernel of a finite monoid is a generalization of that of the derived subgroup of a finite group. A monoid $M$ is then called solvable if its chain of Abelian kernels terminates with the submonoid of $M$ generated by its idempotents. The main result of this paper is that the finite idempotent commuting monoids bearing this property are precisely those whose subgroups are solvable. In particular any finite aperiodic monoid is Abelian-solvable in this sense. A generalization of the main result of this paper has been published [in Int. J. Algebra Comput. 14, No. 5-6, 655-665 (2004; Zbl 1081.20067)] by the authors and ıt S. Margolis and ıt B. Steinberg.

Delgado, Manuel, V{\'ı}tor H. Fernandes, Stuart Margolis, and Benjamin Steinberg. "On semigroups whose idempotent-generated subsemigroup is aperiodic." Internat. J. Algebra Comput.. 14 (2004): 655-665.Website
Delgado, Manuel, and Vítor H. Fernandes. "Abelian kernels of some monoids of injective partial transformations and an application." Semigroup Forum. 61 (2000): 435-452.Website
Delgado, Manuel, and Vítor H. Fernandes. "Abelian kernels of monoids of order-preserving maps and of some of its extensions." Semigroup Forum. 68 (2004): 335-356.Website
Delgado, Manuel, and Vítor H. Fernandes. "Abelian kernels, solvable monoids and the abelian kernel length of a finite monoid." Semigroups and languages. World Sci. Publ., River Edge, NJ, 2004. 68-85.
Dimitrova, I., Vítor H. Fernandes, and J. Koppitz. "The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain." Publicationes Mathematicae Debrecen. 81.1-2 (2012): 11-29.
Dimitrova, I., Vítor H. Fernandes, and J. Koppitz. "A note on generators of the endomorphism semigroup of an infinite countable chain." Journal of Algebra and its Applications (DOI: 10.1142/S0219498817500311). 16 (2017): 1750031 (9 pages). AbstractWebsite

In this note, we consider the semigroup $O(X)$ of all order endomorphisms of an infinite chain $X$ and the subset $J$ of $O(X)$ of all transformations $\alpha$ such that $|Im(\alpha)|=|X|$. For an infinite countable chain $X$, we give a necessary and sufficient condition on $X$ for $O(X) = < J >$ to hold. We also present a sufficient condition on $X$ for $O(X) = < J >$ to hold, for an arbitrary infinite chain $X$.

Dimitrova, I., V. H. Fernandes, J. Koppitz, and T. M. Quinteiro. "Ranks of monoids of endomorphisms of a finite undirected path (DOI: 10.1007/s40840-019-00762-4)." Bulletin of the Malaysian Mathematical Sciences Society (In Press). AbstractWebsite

In this paper we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim is to determine the ranks of the monoids $wEnd P_n$ and $End P_n$ of all weak endomorphisms and all endomorphisms of the undirected path $P_n$ with $n$ vertices. We also consider strong and strong weak endomorphisms of $P_n$.

F
Fernandes, Vítor H., Gracinda M. S. Gomes, and Manuel M. Jesus. "Congruences on monoids of transformations preserving the orientation of a finite chain." J. Algebra. 321 (2009): 743-757.Website
Fernandes, Vítor H., and Jintana Sanwong. "On the rank of semigroups of transformations on a finite set with restricted range." Algebra Colloquium. 21.3 (2014): 497-510.
Fernandes, Vítor H., Gracinda M. S. Gomes, and Manuel M. Jesus. "Presentations for some monoids of partial transformations on a finite chain." Comm. Algebra. 33 (2005): 587-604.Website
Fernandes, Vítor H., and Teresa M. Quinteiro. "On the monoids of transformations that preserve the order and a uniform partition." Communications in Algebra. 39.8 (2011): 2798-2815.
Fernandes, Vítor H., and Paulo G. Santos. "Endomorphisms of semigroups of order-preserving partial transformations." Semigroup Forum (10.1007/s00233-018-9948-z) (In Press). AbstractWebsite

In this paper we characterize the monoids of endomorphisms of the semigroups PO_n and POI_n of all order-preserving partial transformations and of all order-preserving partial permutations, respectively, of a finite n-chain.

Fernandes, Vitor H. "Semigroups of order preserving mappings on a finite chain: a new class of divisors." Semigroup Forum. 54 (1997): 230-236.Website
Fernandes, Vítor H., and Teresa M. Quinteiro. "A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutations." Bull. Korean Math. Soc.. 53.2 (2016): 495-506. AbstractWebsite

In this note we consider the monoid $PODI_n$ of all monotone partial permutations on $\{1,\ldots,n\}$ and its submonoids $DP_n$, $POI_n$ and $ODP_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $POI_n$ and $ODP_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $PODI_n$ is a quotient of a semidirect product of $POI_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $DP_n$ is a quotient of a semidirect product of $ODP_n$ and $\mathcal{C}_2$.

Fernandes, Vítor H. "On divisors of pseudovarieties generated by some classes of full transformation semigroups." Algebra Colloq.. 15 (2008): 581-588.
Fernandes, V. H., and M. V. Volkov. "On divisors of semigroups of order-preserving mappings of a finite chain." Semigroup Forum. 81 (2010): 551-554.Website