Faculty of Mathematics and Computer Science

Universal algebras (1) |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

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. |