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

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

Noetherian Tensor Products

1972 ◽  
Vol 15 (2) ◽  
pp. 235-238
Author(s):  
E. A. Magarian ◽  
J. L. Motto
Keyword(s):  
Tensor Product ◽  
Jacobson Radical ◽  
Tensor Products ◽  
Minimum Condition ◽  
Ideal Structure ◽  
The Ideal

Relatively little is known about the ideal structure of A⊗RA' when A and A' are R-algebras. In [4, p. 460], Curtis and Reiner gave conditions that imply certain tensor products are semi-simple with minimum condition. Herstein considered when the tensor product has zero Jacobson radical in [6, p. 43]. Jacobson [7, p. 114] studied tensor products with no two-sided ideals, and Rosenberg and Zelinsky investigated semi-primary tensor products in [9].All rings considered in this paper are assumed to be commutative with identity. Furthermore, R will always denote a field.

scholarly journals Near-rings of continuous functions on disconnected groups

1979 ◽  
Vol 28 (4) ◽  
pp. 433-451 ◽  
Author(s):  
Robert D. Hofer
Keyword(s):  
Topological Group ◽  
Identity Element ◽  
Continuous Functions ◽  
Ideal Structure ◽  
Rings Of Continuous Functions ◽  
The Ideal

AbstractN(G) denotes the near-ring of all continuous selfmaps of the topological group G (under composition and the pointwise induced operation) and N0(G) is the subnear-ring of N(G) consisting of all functions having the identity element of G fixed. It is known that if G is discrete then (a) N0(G) is simple and (b) N(G) is simple if and only if G is not of order 2. We begin a study of the ideal structure of these near-rings when G is a disconnected group.

Ideal and Real Structure of Ti5O4(PO4)4: X-ray and HRTEM Investigations

1998 ◽  
Vol 54 (6) ◽  
pp. 722-731 ◽  
Author(s):  
F. Reinauer ◽  
R. Glaum
Keyword(s):  
Crystal Structure ◽  
Electron Microscopy ◽  
Structure Refinement ◽  
Ideal Structure ◽  
Crystal Data ◽  
Asymmetric Unit ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
The Ideal

The crystal structure of pentatitanium tetraoxide tetrakis(phosphate), Ti5O4(PO4)4, has been determined and refined from X-ray diffraction single-crystal data [P212121 (No. 19), Z = 4, a = 12.8417 (12), b = 14.4195 (13), c = 7.4622 (9) Å (from Guinier photographs); conventional residual R 1 = 0.042 for 2556 Fo > 4σ(Fo ), R 1 = 0.057 for all 3276 independent reflections; 282 parameters; 29 atoms in the asymmetric unit of the ideal structure]. The structure is closely related to those of β-Fe2O(PO4)-type phosphates and synthetic lipscombite, Fe3(PO4)4(OH). While these consist of infinite chains of face-sharing MO6 octahedra, in pentatitanium tetraoxide tetrakis(phosphate) only five-eighths of the octahedral voids are occupied according to □3Ti5O4(PO4)4. Four of the five independent Ti4+O6 show high radial distortion [1.72 ≤ d(Ti−O) ≤ 2.39 Å] and a typical 1 + 4 + 1 distance distribution. The fifth Ti4+O6 is an almost regular octahedron [1.91 ≤ d(Ti−O) ≤ 1.98 Å]. Partial disorder of Ti4+ over the available octahedral voids is revealed by the X-ray structure refinement. High-resolution transmission electron microscopy (HRTEM) investigations confirm this result.

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