scholarly journals On the prime ideal structure of symbolic Rees algebras

2012 ◽  
Vol 4 (3) ◽  
pp. 327-343
Author(s):  
S. Bouchiba ◽  
S. Kabbaj
Keyword(s):  
Prime Ideal ◽  
Ideal Structure ◽  
Rees Algebras

Some Characterizations of The Projection Property in Archimedean Riesz Spaces

1972 ◽  
Vol 24 (2) ◽  
pp. 306-311 ◽  
Author(s):  
K. K. Kutty ◽  
J. Quinn
Keyword(s):  
Band Structure ◽  
Prime Ideal ◽  
Vector Lattice ◽  
Strong Relationship ◽  
Ideal Structure ◽  
Projection Property ◽  
Dedekind Completion ◽  
Riesz Spaces

In this paper we give some new characterizations of the projection property in Archimedean Riesz spaces. Our approach primarily explores the interrelationships between such things as the band structure or the prime ideal structure of an Archimedean vector lattice and corresponding structures of its Dedekind completion. Our results show that, in general, there is a ‘strong“ relationship if and only if the original vector lattice has the projection property. The main result of this paper is Theorem 2.6 which both summarizes and extends all of the results we obtain prior to it.

scholarly journals The prime ideal structure of the Minkowski ring of polytopes

1992 ◽  
Vol 78 (3) ◽  
pp. 239-251 ◽  
Author(s):  
Klaus G. Fischer ◽  
Jay Shapiro
Keyword(s):  
Prime Ideal ◽  
Ideal Structure

scholarly journals On the prime ideal structure of tensor products of algebras

2002 ◽  
Vol 176 (2-3) ◽  
pp. 89-112 ◽  
Author(s):  
Samir Bouchiba ◽  
David E. Dobbs ◽  
Salah-Eddine Kabbaj
Keyword(s):  
Prime Ideal ◽  
Tensor Products ◽  
Ideal Structure

scholarly journals Prime ideals in skew Laurent polynomial rings

1993 ◽  
Vol 36 (2) ◽  
pp. 299-317 ◽  
Author(s):  
K. W. Mackenzie
Keyword(s):  
Prime Ideal ◽  
Polynomial Ring ◽  
Commutative Algebra ◽  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Prime Ideals ◽  
Ideal Structure ◽  
Locally Finite ◽  
Finite Dimensional ◽  
Laurent Polynomial Ring

Let R be a commutative ring and {σ1,…,σn} a set of commuting automorphisms of R. Let T = be the skew Laurent polynomial ring in n indeterminates over R and let be the Laurent polynomial ring in n central indeterminates over R. There is an isomorphism φ of right R-modules between T and S given by φ(θj) = xj. We will show that the map φ induces a bijection between the prime ideals of T and the Γ-prime ideals of S, where Γ is a certain set of endomorphisms of the ℤ-module S. We can study the structure of the lattice of Γ-prime ideals of the ring S by using commutative algebra, and this allows us to deduce results about the prime ideal structure of the ring T. As an example, if R is a Cohen-Macaulay ℂ-algebra and the action of the σj on R is locally finite-dimensional, we will show that the ring T is catenary.

On the Prime Ideal Structure of Bhargava Rings

2010 ◽  
Vol 38 (4) ◽  
pp. 1385-1400 ◽  
Author(s):  
I. Alrasasi ◽  
L. Izelgue
Keyword(s):  
Prime Ideal ◽  
Ideal Structure

ON CONJUGATE PRIME IDEALS OF TENSOR PRODUCTS OF k-ALGEBRAS

2010 ◽  
Vol 09 (01) ◽  
pp. 1-10 ◽  
Author(s):  
SAMIR BOUCHIBA
Keyword(s):  
Prime Ideal ◽  
Galois Theory ◽  
Tensor Products ◽  
Field Extension ◽  
Prime Ideals ◽  
Dimension Theory ◽  
Ideal Structure ◽  
Normal Field ◽  
Minimal Prime

The purpose of this paper is to explore new aspects of the prime ideal structure of tensor products of algebras over a field k. We prove that given a k-algebra A and a normal field extension K of k (in the sense of Galois theory), then for any prime ideals P1 and P2 of K ⊗k A lying over a fixed prime ideal p of A, there exists a k-automorphism σ of K such that (σ ⊗k id A)(P1) = P2. As an Application, we establish a result related to the dimension theory of tensor products stating that, for two arbitrary k-algebras A and B, the minimal prime ideals of p ⊗k B + Aσk q have the same height, for any prime ideals p and q of A and B, respectively.

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