On essential left ideals of associative rings.
On Euclidean Algorithms With Some Particular Properties
On exactness of long sequences of homology semimodules.
On existing of filtered multiplicative bases in group algebras.
On faithful projective representations of finite abelian p-groups over a field of characteristic p
Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.
On feebly nil-clean rings
A ring is feebly nil-clean if for any there exist two orthogonal idempotents and a nilpotent such that . Let be a 2-primal feebly nil-clean ring. We prove that every matrix ring over is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.
On filial rings
On Filtered Modules and their Associated Graded Modules.
On FI-mono-retractable modules
We introduce the notion of FI-mono-retractable modules which is a generalization of compressible modules. We investigate the properties of such modules. It is shown that the rings over which every cyclic module is FI-mono-retractable are simple Noetherian -ring with zero socle or Artinian semisimple. The last section of the paper is devoted to the endomorphism rings of FI-retractable modules.
On finite homomorphic images of the multiplicative group of a division algebra.
On Finitely Generated Flat Modules II.
On Finitely Generated Flat Modules III.
On finitely generated n-SG-projective modules
We prove that finitely generated n-SG-projective modules are infinitely presented.
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 finiteness of rings with finite maximal subrings.
On flat covers in varieties
Flat covers do not exist in all varieties. We give a necessary condition for the existence of flat covers and some examples of varieties where not all algebras have flat covers.
On Flatness and Projectivity of a Ring as a Module over a Fixed Subring.
On Free Quadratic Extensions of Rings.
On free ring extensions of degree n.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...