Add to ORKGAbstract In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore extension R[χ, δ,d], then I is closed and principal generated by a normal polynomial of minimal degree if and only if I contains a Sharma polynomial of minimal degree. KEYWORDS: principal ideals, Sharma polynomials, Ore extensions. PRINCIPAL IDEALS IN ORE EXTENSIONS Wagner CORTES and Miguel FERRERO Abstract. In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore extension R[x; σ, d], then I is closed and principal generated by a normal polynomial of minimal degree if and only if I contains a Sharma polynomial of minimal degree
The concept of prime ideals and its generalizations have a distinguished place in commutative algeb...
A well known result on polynomial rings states that, for a given ring $R$, if $R$ has no non-zero ni...
In this article, Ore extensions of the class of G-Dedekind prime rings satisfying a polynomial ident...
Abstract. In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore ex...
In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore extension R[...
AbstractFor a module MR we compute the set of associated primes of M[x;σ] over the left Ore extensio...
In these notes we introduce minimal prime ideals and some of their applications. We prove Krull's pr...
This thesis deals with a class of rings known as Ore extensions. An Ore extension can be described a...
We give a self-contained proof of a general conjecture of G. Gras on principalization of ideals in a...
AbstractThe main theorem of this article is an extension of the generalized principal ideal theorem ...
Corrigendum to minimal prime ideals of Ore Extension over a commutative Dedekind domain and its appl...
Let $R$ be a right Noetherian ring which is also an algebra over $\mathbb{Q}$ ($\mathbb{Q}$ the fiel...
is a cyclic R-module, then I + J = R. The rings R such that R/I ⊕R/J is a cyclic R-module for all di...
A ring R is said to be prime if AB = 0 implies A= 0 or B = 0 for any (two sided) ideals A, B of R. I...
Abstract. Given a pair of commutative rings R ( T with the same identity, T is a minimal ring extens...
The concept of prime ideals and its generalizations have a distinguished place in commutative algeb...
A well known result on polynomial rings states that, for a given ring $R$, if $R$ has no non-zero ni...
In this article, Ore extensions of the class of G-Dedekind prime rings satisfying a polynomial ident...
Abstract. In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore ex...
In this paper we prove that if R is a prime ring and I is an R-disjoint ideal of an Ore extension R[...
AbstractFor a module MR we compute the set of associated primes of M[x;σ] over the left Ore extensio...
In these notes we introduce minimal prime ideals and some of their applications. We prove Krull's pr...
This thesis deals with a class of rings known as Ore extensions. An Ore extension can be described a...
We give a self-contained proof of a general conjecture of G. Gras on principalization of ideals in a...
AbstractThe main theorem of this article is an extension of the generalized principal ideal theorem ...
Corrigendum to minimal prime ideals of Ore Extension over a commutative Dedekind domain and its appl...
Let $R$ be a right Noetherian ring which is also an algebra over $\mathbb{Q}$ ($\mathbb{Q}$ the fiel...
is a cyclic R-module, then I + J = R. The rings R such that R/I ⊕R/J is a cyclic R-module for all di...
A ring R is said to be prime if AB = 0 implies A= 0 or B = 0 for any (two sided) ideals A, B of R. I...
Abstract. Given a pair of commutative rings R ( T with the same identity, T is a minimal ring extens...
The concept of prime ideals and its generalizations have a distinguished place in commutative algeb...
A well known result on polynomial rings states that, for a given ring $R$, if $R$ has no non-zero ni...
In this article, Ore extensions of the class of G-Dedekind prime rings satisfying a polynomial ident...