More on matrix near-rings.
More on the Schur group of a commutative ring.
Most abelian p-groups are determined by the Jacobson radical of their endomorphism rings.
Multiparameter quantum function algebra at roots of 1.
-Koszul algebras, a summary.
Near loop rings of Moufang loops.
Necklace rings and their radicals.
Nil right ideals in inverse semigroup algebras.
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...
Nil-extensions of completely simple semirings
A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.
Nilpotent blocks and their source algebras.
Nilpotent Elements in Group Rings.
Noncommutative algebraic geometry.
The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure. In this paper we shall show that one may overcome these difficulties by introducing a noncommutative algebraic geometry, where affine schemes are modeled...
Noncommutative algebraic geometry: From pi-algebras to quantum groups.
Noncommutative analogs of symmetric polynomials
Noncommutative deformations of modules.
Non-commutative reduction rings.
Non-commutative rings of fractions in algebraical approach to control theory
Non-commutative separability and group actions.
We give conditions for the skew group ring S * G to be strongly separable and H-separable over the ring S. In particular we show that the H-separability is equivalent to S being central Galois extension. We also look into the H-separability of the ring S over the fixed subring R under a faithful action of a group G. We show that such a chain: S * G H-separable over S and S H-separable over R cannot occur, and that the centralizer of R in S is an Azumaya algebra in the presence of a central element...
Non-holonomic modules over Weyl algebras and enveloping algebras.