| title: | Selected polynomial completeness problems in algebra |
|---|---|
| reg no: | ETF5368 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.1-1.5. Exact Sciences |
| status: | completed |
| institution: | TU Faculty of Mathematics |
| head of project: | Kalle Kaarli |
| duration: | 01.01.2003 - 31.12.2005 |
| description: | The aim of the project is to continue the study of different aspects of polynomial completeness of algebras. This time we wish to focus on certain selected problems which have come up in the course of work on earlier research projects but have remained unsolved mainly because of lack of time. The earlier treatment of these problems as well as the recent analysis have created the conviction that all of them are still of considerable importance and interest. Besides, the likelyhood that we are able to solve them is high. More concretely, our problems and working hypotheses are the following: 1. Describe, at least in congruence rigid case, the categorical equivalence classes of finite algebras which have no proper subalgebras and generate arithmetical varieties. The hypothesis is that such classes are in 1-1 correspondence with pairs (G,r) where G is a group scheme and r is a certain equivalence relation on the lattice of the group scheme. 2. To try to solve the endoprimality problem of abelian groups with unbounded torsion part and of torsionfree rank 1. We expect that the most of such groups should be endoprimal. In case of torsionfree abelian groups of finite rank to determine how the endoprimality of group A depends on the structure of R-module V. Here V and R are injective envelopes of A and the additive group of its endomorphism ring, respectively. Note that V is a vector space over the field of rationals Q and R is a Q-algebra. We expect that the answer can be given in terms of the radical of R. 3. To describe modular order affine complete lattices of finite heigth. As the main step, to make clear which subdirect products of two simple modular complemented lattices of finite heigth are order affine complete. 4. To find out which varieties of distributive Ockham algebras have "good" theory of local polynomial functions. There is a reason to believe that there exists a largest variety with such property which can be characterized by a certain property of subdirectly irreducibles. To construct affine completions of Stone and Kleene algebras. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Kalle Kaarli | TU Faculty of Mathematics | Professor | |
| 2. | Vladimir Kutšmei | Univ. of Tartu, Inst.of Pure Math. | 1/2 researcher, doctoral student | |