Ideal structure in radical sequence algebras

1983 ◽  
pp. 248-257 ◽  
Author(s):  
K. B. Laursen
Keyword(s):  
Ideal Structure

The ideal structure of XX

1984 ◽  
Vol 30 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Neil Hindman ◽  
Paul Milnes
Keyword(s):  
Ideal Structure ◽  
The Ideal

scholarly journals Falling -Ideals in -Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Young Bae Jun ◽  
Sun Shin Ahn ◽  
Kyoung Ja Lee
Keyword(s):  
Theoretical Approach ◽  
Ideal Structure ◽  
Fundamental Properties ◽  
The Ideal

Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in -algebras is established. The notions of a falling -subalgebra, a falling -ideal, a falling -ideal, and a falling -ideal of a -algebra are introduced. Some fundamental properties are investigated. Relations among a falling -subalgebra, a falling -ideal, a falling -ideal, and a falling -ideal are stated. Characterizations of falling -ideals and falling -ideals are discussed. A relation between a fuzzy -subalgebra and a falling -subalgebra is provided.

scholarly journals The ideal structure of the Hecke $C^*$ -algebra of Bost and Connes

2000 ◽  
Vol 318 (3) ◽  
pp. 433-451 ◽  
Author(s):  
Marcelo Laca ◽  
Iain Raeburn
Keyword(s):  
Ideal Structure ◽  
C Algebra ◽  
The Ideal

scholarly journals Boundary quotients of the right Toeplitz algebra of the affine semigroup over the natural numbers

10.53733/90 ◽  
2021 ◽  
Vol 52 ◽  
pp. 109-143
Author(s):  
Astrid An Huef ◽  
Marcelo Laca ◽  
Iain Raeburn
Keyword(s):  
Regular Representation ◽  
Crossed Product ◽  
Ideal Structure ◽  
Toeplitz Algebra ◽  
Natural Numbers ◽  
Kms States ◽  
C Algebra ◽  
Affine Semigroup ◽  
Natural Dynamics ◽  
The Right

We study the Toeplitz $C^*$-algebra generated by the right-regular representation of the semigroup ${\mathbb N \rtimes \mathbb N^\times}$, which we call the right Toeplitz algebra. We analyse its structure by studying three distinguished quotients. We show that the multiplicative boundary quotient is isomorphic to a crossed product of the Toeplitz algebra of the additive rationals by an action of the multiplicative rationals, and study its ideal structure. The Crisp--Laca boundary quotient is isomorphic to the $C^*$-algebra of the group ${\mathbb Q_+^\times}\!\! \ltimes \mathbb Q$. There is a natural dynamics on the right Toeplitz algebra and all its KMS states factor through the additive boundary quotient. We describe the KMS simplex for inverse temperatures greater than one.

A Note on the Ideal Structure of C(X)

1969 ◽  
Vol 23 (1) ◽  
pp. 174 ◽  
Author(s):  
William E. Dietrich
Keyword(s):  
Ideal Structure ◽  
The Ideal
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