"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Universal algebras (1)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MA251
1
2+2+0
9
compulsory
Algebră şi Geometrie
Teaching Staff in Charge
Prof. PURDEA Ioan, Ph.D., purdea@math.ubbcluj.ro
Aims
The study of notions and basic results of the theory of universal algebras.
Content
Lattice, complete lattice. Closure sistems and closure operators. Algebraic closure systems and operators. Semilattice, ideals in semilattices. Modular lattice, distributive lattice, boolean lattice. Representation theorems for distributive lattices and boolean lattices. Boolean rings. The lattice of subalgebras of a universal algebra. The lattice of congruences of a universal algebra. Homomorphic relations. Quotient algebra. The isomorphism theorems for universal algebras. Polynomials over universal algebras and
polynomial symbols (words). Groups with multioperators. Normal series and composition series. Invariant series and principal series. Abelian, nilpotent and solvable groups with multioperators.
References
1. Burris, S., Sankappanavar, H.P., A Course in Universal Algebra, Springer-Verlag, 1994
2. Cohn, P.M., Universal Algebra, Harper and Row, New York, 1965
3. Gratzer, G., Universal Algebra, Springer-Verlag, 1989
4. Purdea, I., Pic, Gh., Tratat de algebra moderna, vol.I, Ed. Academiei, 1977
5. Purdea, I., Tratat de algebra moderna, vol.II, Ed. Academiei, 1982
Assessment
Written exam.