Publications

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2005
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.

2004
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.
Fernandes, Vítor H., Gracinda M. S. Gomes, and Manuel M. Jesus. "Presentations for some monoids of injective partial transformations on a finite chain." Southeast Asian Bull. Math.. 28 (2004): 903-918.
Semigroups and languages. Eds. Isabel M. Araújo, Mário J. J. Branco, V{\'ı}tor H. Fernandes, and Gracinda M. S. Gomes. Proceedings of the workshop held at the University of Lisbon, Lisboa, November 27–29, 2002. River Edge, NJ: World Scientific Publishing Co. Inc., 2004.
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
2002
Fernandes, Vítor H. "Presentations for some monoids of partial transformations on a finite chain: a survey." Semigroups, algorithms, automata and languages (Coimbra, 2001). World Sci. Publ., River Edge, NJ, 2002. 363-378.
Fernandesh, V. U. "A new class of divisors of semigroups of isotone mappings of finite chains." Izv. Vyssh. Uchebn. Zaved. Mat. (2002): 51-59.
2001
Fernandes, Vitor H. "A division theorem for the pseudovariety generated by semigroups of orientation preserving transformations on a finite chain." Comm. Algebra. 29 (2001): 451-456.Website
Fernandes, V. H. "The monoid of all injective order preserving partial transformations on a finite chain." Semigroup Forum. 62 (2001): 178-204.
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.
2000
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
Fernandes, Vitor H. "The monoid of all injective orientation preserving partial transformations on a finite chain." Comm. Algebra. 28 (2000): 3401-3426.Website
1998
Fernandes, Vitor H. "Normally ordered inverse semigroups." Semigroup Forum. 56 (1998): 418-433.Website
1997
Fernandes, Vitor H. "Semigroups of order preserving mappings on a finite chain: a new class of divisors." Semigroup Forum. 54 (1997): 230-236.Website