Near Domains of Composite Characteristic.
Near Integral Domains on Nonabelian Groups.
Nil-clean and unit-regular elements in certain subrings of
An element in a ring is clean (or, unit-regular) if it is the sum (or, the product) of an idempotent and a unit, and is nil-clean if it is the sum of an idempotent and a nilpotent. Firstly, we show that Jacobson’s lemma does not hold for nil-clean elements in a ring, answering a question posed by Koşan, Wang and Zhou (2016). Secondly, we present new counter-examples to Diesl’s question whether a nil-clean element is clean in a ring. Lastly, we give new examples of unit-regular elements that are...
Nilpotent blocks and their source algebras.
Non commutative Krull domains.
Noncommutative graded domains with quadratic.
Non-commutative rings of fractions in algebraical approach to control theory
Noncommutative Valuation Rings
Noncommutativity and noncentral zero divisors.
Normability of an S-ring.
We give some criteria of normability of an S-ring, and we study the properties of its norms.
Note on strongly nil clean elements in rings
Let be an associative unital ring and let be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
Notes on -derivations.
On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings.
On a subset with nilpotent values in a prime ring with derivation
Let be a prime ring, with no non-zero nil right ideal, a non-zero drivation of , a non-zero two-sided ideal of . If, for any , , there exists such that , then is commutative. As a consequence we extend the result to Lie ideals.
On a theorem of McCoy
We study McCoy’s theorem to the skew Hurwitz series ring for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring satisfies McCoy’s theorem of skew Hurwitz series.
On Anti-inverse Rings
On anti-inverse rings.
On center-like elements in rings.
On centralizers of semiprime rings
Let be a semiprime ring and an additive mapping such that holds for all . Then is a left centralizer of . It is also proved that Jordan centralizers and centralizers of coincide.
On clean ideals.