On a refinement in the classification of the nil rings
On commutativity of rings with constraints on subsets
On filial rings
On finiteness conditions for subalgebras with zero multiplication
Let F be a commutative ring with unit. In this paper, for an associative F-algebra A we study some properties forced by finite length or DCC condition on F-submodules of A that are subalgebras with zero multiplication. Such conditions were considered earlier when F was either a field or the ring of rational integers. In the final section, we consider algebras with maximal commutative subalgebras of finite length as F-modules and obtain some results parallel to those known for ACC condition or finite...
On group nil rings
On Kolchin's theorem.
A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent.Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite dimensional algebra...
On non-Spechtianness of the variety of associative rings that satisfy the identity .
On periodic rings.
On rings with zero total.
On some commutativity theorems for finite rings and finite groups
On some Results Related to Köthe's Conjecture
The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.
On some weakly supernilpotent radicals of rings
On strongly 0-prime ideals in near-rings.
On structure of certain periodic rings and near-rings.
On the Classification of Nilpotent Groups.
On the degree of nilpotency of the radical of relatively free algebras.
On the Isomorphism Problem for Integral Group-Rings of Circle-Groups.
On the Jacobson radical of graded rings
All commutative semigroups are described such that the Jacobson radical is homogeneous in each ring graded by .
On the Jacobson radical of strongly group graded rings
For any non-torsion group with identity , we construct a strongly -graded ring such that the Jacobson radical is locally nilpotent, but is not locally nilpotent. This answers a question posed by Puczyłowski.
On the nilpotency of the Jacobson radical of semigroup rings.