| title: | Partially ordered acts and biacts |
|---|---|
| reg no: | ETF6238 |
| project type: | Estonian Science Foundation research grant |
| status: | accepted |
| institution: | University of Tartu |
| head of project: | Mati Kilp |
| duration: | 01.01.2005 - 31.12.2008 |
| description: | Following results of the articles [Fakhruddin, S. M., Absolute flatness and amalgams in pomonoids, Semigroup Forum 33, 1986, 15-22] and [Shi, X., Liu, Z., Wang, F. and S. Bulman-Fleming, Indecomposable, projective and flat S-posets, Comm. Algebra, to appear] it is planned to investigate flatness properties of partially ordered acts (S-posets) over partially ordered monoids S. As the authors of these papers have generalised concepts of the theory of ordinary (i.e. unordered) acts in different ways, the first task is to fix the most suitable set of concepts for this situation. It is possible that several versions of flatness theory arise (for example depending on whether one requires convexity of subacts or not). In this analyses it is planned to consider all main types of flatness starting from torsion freeness until freeness (see [Kilp, M., Knauer U. and A. V. Mikhalev, Monoids, Acts and Categories, Walter de Gruyter, Berlin, New York, 2000]) and their generalisations considered later (see [Bulman-Fleming, S., Kilp, M., Equalizers and flatness properties of acts, Communications in Algebra 30, 2002, 1475-1498], [Laan, V., Pullbacks and flatness properties of acts I, Comm. Algebra 29 (2), 2001, 829-850] ). Biacts (and perhaps also partially ordered biacts) over two different monoids are special cases of certain functors, so called distributors. Tensor multiplication by biacts has an important role in two fields: descent theory and investigations of Morita equivalence. It will be tried to generalise the results proved using biacts (e.g. in [Laan, V., On descent theory for monoid actions, Theory Appl. Categories, to appear] and [Knauer, U., Morita Äquivalenz von Halbgruppen, dissertation, Bielefeld, 1971]) to the case of distributors. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Mati Kilp | University of Tartu | professor | |
| 2. | Valdis Laan | University of Tartu | Senior Researcher | |