Action-type axiomatizable classes of group representations

Journal of Mathematical Sciences - Tập 142 - Trang 1915-1922 - 2007
A. Gvaramia1, B. Plotkin2
1Abhazia State University, Suhum, Abhazia
2Hebrew University, Jerusalem, Israel

Tóm tắt

The paper adjoins the work of B. I. Plotkin and S. M. Vovsi, Varieties of Representations of Groups (Zinatne, Riga (1983)), and turns out to be, in a sense, its continuation. In the former, the varieties of representations have been considered. As a matter of fact, the varieties under consideration are action-type varieties. This paper studies other classes of representations, axiomatizable in a special action-type logic.

Tài liệu tham khảo

G. Gratzer and H. Lakser, “A note on the implicational class generated by a class of structures,” Can. Math. Bull., 16, No. 4, 603–605 (1974). A. Gvaramia, “Maltsev’s theorem on quasi-varieties for multi-sorted algebras,” in: Algebra and Discrete Mathematics, Riga (1984), pp. 33–45. A. I. Maltsev, Algebraic Systems [in Russian], Nauka, Moscow (1970). B. I. Plotkin and A. Tsurkov, Action-Type Algebraic Geometry on Group Representations, Preprint. B. I. Plotkin and S. M. Vovsi, Varieties of Representations of Groups [in Russian], Zinatne, Riga (1983).