Abstract
Local Finite basis property and local representability for varieties of associative rings has been reported. The finite-dimensional algebra A i (the intermediate support) is described by a set of induction parameters, and it does not include any nonzero ideals with nonzero intersection. Consideration of 1-generated subalgebras enables one to prove that a representation of an algebra can be reduced to the following form. A representable algebra can be considered as a sheaf of finite-dimensional algebras on an affine space. The relation between languages of quivers, gradings and identities enables us, in particular, to consider effects of multiplicities of cells and to construct systems of pushing substitutions as well as external ideals. There is an algorithm for constructing a maximal system of disjoint projectively minimal ideals for an intermediate support.
| Original language | English |
|---|---|
| Pages (from-to) | 458-461 |
| Number of pages | 4 |
| Journal | Doklady Mathematics |
| Volume | 81 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 2010 |
Bibliographical note
Funding Information:The author is grateful for support to V.N. Latyshev and A.V. Mikhalev, the leaders of the seminar for ring theory in MSU, where this work was presented, and to A.V. Grishin, K.A. Zubrilin, V.T. Markov, S.V. Pche lintsev, V.V. Shchigolev and to all participants of the seminar for stimulating discussion. The author is thankful to A.R. Kemer, L.M. Samoilov, L.A. Bokut’, A. Mekey for useful remarks. The work was fulfilled under the support by ISF (grant no. 1178/06). It was also partially supported by the Russian Foundation for Basic Research (grant no. 08 01 91300 a).