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An intermediate ring between a polynomial ring and a power series ring

M. Tamer Koşan, Tsiu-Kwen Lee, Yiqiang Zhou (2013)

Colloquium Mathematicae

Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]: [R;I][x]: = ∑ i ≥ 0 r i x i ∈ R [ [ x ] ] : ∃ 0 ≤ n∈ ℤ such that r i ∈ I , ∀ i ≥ n. The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with a certain ring...

An observation on Krull and derived dimensions of some topological lattices

M. Rostami, Ilda I. Rodrigues (2011)

Archivum Mathematicum

Let ( L , ≤ ) , be an algebraic lattice. It is well-known that ( L , ≤ ) with its topological structure is topologically scattered if and only if ( L , ≤ ) is ordered scattered with respect to its algebraic structure. In this note we prove that, if L is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then L has Krull-dimension if and only if L has derived dimension. We also prove the same result for error L , the set of all prime elements of L . Hence the dimensions on the lattice...

Anneaux Corpomorphes

Jeanne Ferentinou-Nicolacopoulou (1976)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Anneaux semi-artiniens

Constantin Năstăsescu, Nicolae Popescu (1968)

Bulletin de la Société Mathématique de France

Annihilating and power-commuting generalized skew derivations on Lie ideals in prime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

Let R be a prime ring of characteristic different from 2 and 3, Q r its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R . An additive map D : R → R is called an α -derivation (or a skew derivation) on R if D ( x y ) = D ( x ) y + α ( x ) D ( y ) for all x , y ∈ R . An additive mapping F : R → R is called a generalized α -derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F ( x y ) = F ( x ) y + α ( x ) D ( y ) for all x , y ∈ R . We prove that, if F ...

Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 )

Yu Wang, Xiaoming Li (2023)

Czechoslovak Mathematical Journal

Let U be the two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 ) and F ( U ) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F ( U ) in the case when r s - 1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.

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