PROJECT 04M03B Algebra |
Several branches of algebra will be studied. In analytic number theory zeta function will be studied, Riemann zeta function in particular as well as some similar functions and the multiplicative number theory in general. Various arithmetical functions will also be studied. In group theory presentability of classical groups will be studied. For universal algebras the corresponding varieties will be investigated using the associated lattices as well as word problems for varieties of algebras. Fuzzy algebras and congruences of fuzzy sets and systems will also be considered. Several theories of semigroup decomposition (semilattice and orthogonal) will be studied as well as the lattice of semigroup relations and the representation of distinguished elements of the lattice.
Moreover semigroup representations, constructions of special types of semigroups, identities and varieties of semigroups as well as lattices of varieties and semigroup and polynomial identities of a ring will also be studied. Connected with this is the search for corresponding algorithms and new languages and with applications to computer science. Some research will be directed towards applications of linear algebra to mathematical chemistry.