A note on rings with certain variable identities.
A note on semiprime rings with derivation.
A note on the isomorphism of modular group algebras of -mixed Abelian groups with divisible -components.
A Note On Units And Divisors Of Zero In Group Rings
A remark concerning commutativity modulo radical in Banach algebras
A result of commutativity of rings.
A subclass of strongly clean rings
In this paper, we introduce a subclass of strongly clean rings. Let be a ring with identity, be the Jacobson radical of , and let denote the set of all elements of which are nilpotent in . An element is called very -clean provided that there exists an idempotent such that and or is an element of . A ring is said to be very -clean in case every element in is very -clean. We prove that every very -clean ring is strongly -rad clean and has stable range one. It is shown...
A Survey of Rings Generated by Units
This article presents a brief survey of the work done on rings generated by their units.
A theoreme on derivations in semiprime rings.
A weak periodicity condition for rings.
Abelian modules.
Addendum to “Ring elements as sums of units”
We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].
Admissible groups, symmetric factor sets, and simple algebras.
Algebraic analysis in structures with the Kaplansky-Jacobson property
In 1950 N. Jacobson proved that if u is an element of a ring with unit such that u has more than one right inverse, then it has infinitely many right inverses. He also mentioned that I. Kaplansky proved this in another way. Recently, K. P. Shum and Y. Q. Gao gave a new (non-constructive) proof of the Kaplansky-Jacobson theorem for monoids admitting a ring structure. We generalize that theorem to monoids without any ring structure and we show the consequences of the generalized Kaplansky-Jacobson...
Almost Abelian rings
A ring is defined to be left almost Abelian if implies for and , where and stand respectively for the set of idempotents and the set of nilpotents of . Some characterizations and properties of such rings are included. It follows that if is a left almost Abelian ring, then is -regular if and only if is an ideal of and is regular. Moreover it is proved that (1) is an Abelian ring if and only if is a left almost Abelian left idempotent reflexive ring. (2) is strongly...
An application of Zassenhaus' unit theorem
An intermediate ring between a polynomial ring and a power series ring
Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]: [R;I][x]: = : ∃ 0 ≤ n∈ ℤ such that , ∀ i ≥ n. The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with a certain ring...
An iteration technique and commutativity of rings.
An observation on Krull and derived dimensions of some topological lattices
Let , be an algebraic lattice. It is well-known that with its topological structure is topologically scattered if and only if is ordered scattered with respect to its algebraic structure. In this note we prove that, if is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then has Krull-dimension if and only if has derived dimension. We also prove the same result for , the set of all prime elements of . Hence the dimensions on the lattice...
Angular distribution of units in abelian group rings - an application to Galois-module theory.