[PDF] Top 20 Nilpotent Elements in Skew Polynomial Rings
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Nilpotent Elements in Skew Polynomial Rings
... nil R x . This condition is strongly connected to the question of whether or not a polynomial ring R x [ ] over a nil ring R is nil, which is related to a question of Amitsur [1]. This is true for any 2-primal ... See full document
16
Skew Polynomial Rings over Weak sigma-rigid Rings and sigma(*)-rings
... of nilpotent elements of a ...σ-rigid rings; Kwak in [10] introduced σ(∗)-rings and Ouyang in [14] introduced weak σ-rigid rings, where σ is an endomorphism of ring ...These ... See full document
7
Skew Polynomial Extensions over Zip Rings
... the skew polynomial rings of automorphism type Rx; σ skew Laurent of polynomial Rx, x −1 ; σ are subrings of Rx; σ Rx, x −1 ; σ whose elements are ... See full document
9
Quasi-duo Partial skew polynomial rings
... Recall that if S is a ring and σ : S → S is an automorphism, an element a ∈ S is said to be σ-nilpotent if for every m ≥ 1 there exists n ≥ 1 such that aσ m (a)σ 2m (a)...σ mn (a) = 0 (see [7] for more details). A ... See full document
11
Skew-Laurent Rings over $\sigma(*)$-rings
... A ring R always means an associative ring with identity 1 6= 0. The set of prime ideals of R is denoted by S pec(R) . The sets of minimal prime ideals of R is denoted by M in.S pec(R) . Prime radical and the set of ... See full document
8
Automorphisms and isomorphisms of Jha Johnson semifields obtained from skew polynomial rings
... Among the semifields with known automorphism groups are the three-dimensional semi- fields over a field of characteristic not 2 (Dickson [13] and Menichetti [24, 25]), and the semifields with 16 elements ... See full document
18
Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings
... free right D-module, in general. The aim of this section is to give two simplicity criteria for GWAs (Theorem 4.2 and Theorem 4.3). The first one (Theorem 4.2) is a simplicity criterion for a GWA A = D[x, y; σ, τ, a] ... See full document
16
Yao
... gave skew cyclic codes defined by using the skew polynomial ring with an automorphism θ over the finite field with q ...non-commutative polynomial rings. Soon afterwards, D. Boucher et ... See full document
6
On Classical Quotient Rings of Skew Armendariz Rings
... the skew polynomial ring whose elements are the polynomials over R, the addition is defined as usual and the multiplication subject to the relation xa = α(a)x + δ(a) for any a ∈ ... See full document
7
Polynomial Rings over Pseudovaluation Rings
... All rings are associative with identity 1. Now let R be a ring. N(R) denotes the set of all nilpotent elements of R. Z(R) denotes the centre of R. Q denotes the field of rational numbers unless ... See full document
6
Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings
... α-rigid rings are reduced i.e., R has no nonzero nilpotent element by Hong et ...α-rigid rings have been studied in Krempa 2, Hirano 4, and Hong et ... See full document
8
Skew polynomial rings and overrings
... I t is straightforward to obtain a characterizatio n in terms of elements of when A (R ,a ) is a quotient ring, but the main object here w ill be to obtain an element-free condition. This is done under the ... See full document
200
On partial skew Armendariz rings
... nonzero nilpotent elements) satisfies this condition, see ...Armendariz rings have been studied by many authors, see [2], [1], [30] and the literature quoted ...of skew Armendariz ... See full document
23
RETRACTED: On Nil and Nilpotent Rings and Modules
... We see that the vector spaces are just special types of modules which arise when the underlying ring is a field. If R is a ring, the definition of an R -module M is closely analogous to the definition of a group action ... See full document
9
On Polynomial Symmetric and Polynomial Skew Symmetric Matrices
... Two polynomial matrices A ( ), B ( ) C m x n ( ) are called right or column equivalent if and only if one of them can be obtained from the other as a result of a finite number of elementary operations ... See full document
5
Noncommutativity and noncentral zero divisors
... 1. Preliminaries. In general, R represents a ring, not necessarily with 1, and Z its center. For Y an element or subset of R, A(Y ) is the two-sided annihilator of Y ; and for H ⊆ R, |H| denotes the cardinal number of H. ... See full document
8
Steadiness of polynomial rings
... that polynomial rings in countably many variables over commutative noetherian rings are ...that polynomial ring T [X] is right steady, if X is countable and T is a skew field finitely ... See full document
11
Nilpotent Elements of Residuated Lattices
... Let F be a filter of A. For all x, y ∈ A, we denote x ≡ y and say that x and y are congruent if and only if x → y ∈ F and y → x ∈ F. ≡ is a congruence relation on A. The quotient residuated lattice with respect to the ... See full document
10
Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ) codes
... are bijective. A division algebra A does not have zero divisors. If A is a finite-dimensional algebra over F , then A is a division algebra over F if and only if A has no zero divisors. 1.2. Skew polynomial ... See full document
21
On Pseudo-valuation rings and their extensions
... Throughout this paper, all rings are associative with identity 1 6 = 0. Let now R be a ring. N (R) denotes the set of all nilpotent elements of R. Z (R) denotes the center of R. Q denotes the field ... See full document
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