arXiv subjects
Publications and source records attributed to E. I. Bunina.
In the given paper we prove that every automorphism of a Chevalley group of type $A_l$, $D_l$, or $E_l$, $l\geqslant 3$, over a commutative local ring without 1/2 is standard, i. e., it is a composition of ring, inner, central and graph automorphisms.
We prove that every isomorphism of Chevalley groups of type $G_2$ over commutative local rings with 1/2 and 1/3 is standard, i. e., it is a composition of a ring isomorphism and an inner automorphism.
In the paper we prove that every automorphism of a (elementary) Chevalley group of type $A_l, D_l$, or $E_l$, $l\geqslant 2$, over a commutative local ring with 1/2 is standard, i. e., is the composition of inner, ring, graph and central automorphisms.
In the paper we prove that every automorphism of a Chevalley group of type $F_4$ over a commutative local ring with~1/2 is standard, i. e., it is a composition of ring and inner automorphisms.
In the paper we prove that every automorphism of and elementary adjoint Chevalley group of types $A_l, D_l$, or $E_l$, over local commutative ring with 1/2 is a composition of a ring automorphism and conjugation by some matrix from the normalizer of the Chevalley group in $\GL(V)$ ($V$ is the adjoint representation space).
In the paper we prove that every automorphism of any adjoint Chevalley group of types B_2 or G_2 is standard, i.e., it is a composition of the ``inner'' automorphism, ring automorphism and central automorphism.
Suppose that R is an ordered ring, G_n(R) is a subsemigroup of $GL_n(R)$, consisting of all matrices with nonnegative elements. A.V. Mikhalev and M.A. Shatalova described all automorphisms of G_n(R), where R is a linearly ordered skewfield and n>1. E.I. Bunina and A.V. Mikhalev found all automorphisms of G_n(R), if R is an arbitrary linearly ordered associative ring with 1/2, n>2. In this paper we describe automorphisms of G_n(R), if R is a commutative partially ordered ring, containing Q, n>2.
It is proved that (elementary) Chevalley groups $G_π(Φ,K)$ and $G_{π'}(Φ',K')$ (or $E_π(Φ,K)$ and $E_{π'}(Φ',K'))$ over infinite fields $K$ and $K'$ of characteristics $\ne 2$, with weight lattices $Λ$ and $Λ'$, respectively, are elementarily equivalent if and only if the root systems $Φ$ and $Φ'$ are isomorphic, the fields $K$ and $K'$ are elementarily equivalent, the lattices $Λ$ and $Λ'$ coincide.
In this paper we study a relationship between elementary equivalence of endomorphism rings of Abelian p-groups and second order equivalence of the corresponding Abelian p-groups.
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of submodules of modules, and automorphism groups of modules.