Complements of Algebra
Cod: 21147
Department: DCET
Scientific area: Mathematics
Total working hours: 156
Total contact time: 26

In this course we study the foundations of the algebraic theory of semigroups.

1. Semigroup theory
2. Completely 0-simples semigroups
3. Regular semigroups
4. Inverse semigroups

By the end of the course the student should be able to prove Green’s Lemmas, Rees’s theorem and the basic results about inverse semigroups.

1. Local structure of semigroups (the structure of a D-class and Green’s Lemmas).
2. The basic results about inverse semigroups.
3. The structure of the most common ransformation semigroups such as T(X) and I(X).

Araújo, João, Mergulhos e coberturas de semigrupos E-unitários, Universiade de Lisboa, 1994.
Higgins, Peter M.(4-ESSX)
Techniques of semigroup theory.
With a foreword by G. B. Preston. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1992. x+258 pp.
Howie, J. M. An introduction to semigroup theory. L.M.S. Monographs, No. 7. Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. x+272 pp.
Howie, John M.
Fundamentals of semigroup theory.
London Mathematical Society Monographs. New Series, 12. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. x+351 pp.
Petrich, Mario Inverse semigroups. Pure and Applied Mathematics (New York). A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1984. x+674 pp.
Rhodes, John; Steinberg, Benjamin The q-theory of finite semigroups. Springer Monographs in Mathematics. Springer, New York, 2009. xxii+666 pp.


Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one final presence-based exam (100%).