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.