Primitive Ideals of Enveloping Algebras Over Commutative Rings

1984 ◽  
Vol 106 (1) ◽  
pp. 113 ◽  
Author(s):  
Ronald S. Irving
Keyword(s):  
Commutative Rings ◽  
Enveloping Algebras ◽  
Primitive Ideals

On the characterization of primitive ideals in enveloping algebras

1980 ◽  
Vol 173 (3) ◽  
pp. 217-221 ◽  
Author(s):  
Ronald S. Irving ◽  
Lance W. Small
Keyword(s):  
Enveloping Algebras ◽  
Primitive Ideals

MULTIPARAMETER QUANTUM FORMS OF THE ENVELOPING ALGEBRA $U_{{\mathfrak g}{\mathfrak l}_N}$ RELATED TO THE FADDEEV-RESHETIKHIN-TAKHTAJAN U(R) CONSTRUCTIONS

1995 ◽  
Vol 04 (02) ◽  
pp. 263-317 ◽  
Author(s):  
JACOB TOWBER
Keyword(s):  
Commutative Rings ◽  
Generators And Relations ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Generating Sets ◽  
Pbw Basis ◽  
Suitable Generalization ◽  
Baxter Operator

Two quantum enveloping algebras UR and ÛR are associated in [RTF] to any Yang-Baxter operator R. These are constructed as subalgebras of A(R)* with specific generating sets. Also, [RTF] construct specific relations on the generators for UR, leaving open the question whether these generate all relations on these generators—let us say R is “perfect” when this is the case. Given an [Formula: see text] -tuple [Formula: see text] of nonzero elements qij,r in the groundfield, ([AST], [R], [S]) construct a multiparameter deformation [Formula: see text] of GLN associated with a Yang-Baxter operator [Formula: see text]. The method of ‘braiding maps’, introduced in [LT], is applied, in order to derive a PBW basis and a generators-and-relations presentation for a suitable generalization of [Formula: see text]. These results imply that [Formula: see text] is perfect, for generic [Formula: see text]. The construction [Formula: see text] is in some ways unsatisfactory if r is a root of 1. A construction [Formula: see text] is proposed, which is in some ways better behaved, coincides with [Formula: see text] if r is not a root of 1, and also makes sense over arbitrary commutative rings.

GENERALIZED OF PRIMARY AVOIDANCE THEOREM FOR COMMUTATIVE RINGS

2018 ◽  
Vol 1 (21) ◽  
pp. 415-438
Author(s):  
Amer Shamil Abdulrhman
Keyword(s):  
Commutative Rings ◽  
Primary Ideals

In this paper we study covering ideals by Cosets of primary ideals and we get a generalized the primary avoidance theorem in the rings which it has been

N-ideals of commutative rings

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2933-2941 ◽  
Author(s):  
Unsal Tekir ◽  
Suat Koc ◽  
Kursat Oral
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Proper Ideal ◽  
Prime Ideals ◽  
Nonzero Identity

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

Sign in / Sign up

Export Citation Format

Share Document