Automorphisms of some structural infinite matrix rings

Differential Polynomial Rings of Triangular Matrix Rings

Some Constructions Related to Rees Matrix Rings

Simple rings with a one-sided minimal ideal may be represented as Rees matrix rings, and conversely. The latter are defined as I ×Λ matrices over a division ring with only a finite number of nonzero entries with certain addition and multiplication. For Rees matrix rings we construct here their isomorphisms, their translational hulls and isomorphisms of the translational hulls, all this in terms...

Some Additive Combinatorics Problems in Matrix Rings

We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers. 2000 Mathematics Subject Classification. 11C20, 11D79, 11T23

Automorphisms of infinite Johnson graphs

Let I be a set of infinite cardinality α. For every cardinality β ≤ α the Johnson graphs Jβ and J are the graphs whose vertices are subsets X ⊂ I satisfying |X | = β , |I \ X | = α and |X | = α, |I \ X | = β (respectively) and vertices X, Y are adjacent if |X \ Y | = |Y \ X | = 1. Note that Jα = J and Jβ is isomorphic to J for every β < α. If β is finite then Jβ and J are connected and it is no...

Some properties of marginal automorphisms of groups

AbstractLet W be a non-empty subset of a free group. The automorphism of a group G is said to be a marginal automorphism, if for all x in G,x^−1alpha(x) in W^*(G), where W^*(G) is the marginal subgroup of G.In this paper, we give necessary and sufficient condition for a purelynon-abelian p-group G, such that the set of all marginal automorphismsof G forms an elementary abelian p-group.