72 citations · 112 across the 8 of their papers we have counts for
9 papers
Automorphisms of categories of free modules and free Lie algebras
R. Lipyanski, B. Plotkin
We prove that the group of automorphisms of the category of free modules over Noterian rings is semi-inner and present also a short proof of a similar result for the variery of Lie…
Action Type Geometrical Equivalence of Representations of Groups
B. Plotkin, A. Tsurkov
For every variety of algebras and every algebras in these variety we can consider an algebraic geometry. Algebras may be many sorted (not necessarily one sorted) algebras. A set of…
On automorphisms of categories of universal algebras
Boris Plotkin, Grigori Zhitomirski
A new approach is suggested to characterize algebraically automorphisms of the category of free algebras of a given variety. It gives in many cases an answer to the problem set by…
Action-type axiomatizable classes of group representations
Boris Plotkin, Aleko Gvaramia
The paper adjoins the book B.Plotkin, S.Vovsi "Varieties of representations of groups", Riga, "Zinatne", 1983, and turns to be, in a sense, its continuation. In the book the variet…
Notes on Engel groups and Engel elements in groups. Some generalizations
Boris Plotkin
Engel groups and Engel elements became popular in 50s. We consider in the paper the more general nil-groups and nil-elements in groups. All these notions are related to nilpotent g…
Algebraic geometry in First Order Logic
B. Plotkin
In every variety of algebras we can consider its logic and its algebraic geometry. In the previous papers geometry in equational logic, i.e., equational geometry has been studi…