-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.
Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra
Let be an arbitrary parabolic subalgebra of a simple associative -algebra. The ideals of are determined completely; Each ideal of is shown to be generated by one element; Every non-linear invertible map on that preserves ideals is described in an explicit formula.
Nonlinear maps preserving Lie products on triangular algebras
In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.
Non-singular covers over monoid rings
We shall introduce the class of strongly cancellative multiplicative monoids which contains the class of all totally ordered cancellative monoids and it is contained in the class of all cancellative monoids. If is a strongly cancellative monoid such that for each and if is a ring such that for each , then the class of all non-singular left -modules is a cover class if and only if the class of all non-singular left -modules is a cover class. These two conditions are also equivalent whenever...
Non-singular covers over ordered monoid rings
Let be a multiplicative monoid. If is a non-singular ring such that the class of all non-singular -modules is a cover class, then the class of all non-singular -modules is a cover class. These two conditions are equivalent whenever is a well-ordered cancellative monoid such that for all elements with there is such that . For a totally ordered cancellative monoid the equalities and hold, being Goldie’s torsion theory.