Universal algebras (2) |
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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 |
Derived algebras. The monoid of endomorphisms and the group of automorphisms of a universal algebra. Constructions of universal algebras: direct products, subdirect products, direct limits and inverse limits. Operators on classes of universal algebras. Varieties of universal algebras. Free universal algebras. Identities and free algebras. Varieties of algebras with commuting congruences. Independence in universal algebras. Independent subsets, bases. Problems on cardinals of bases. Independence in special classes of algebras. |
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. |