Decompositions of a C -algebra

G. C. Rao and P. Sundarayya

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-8

Abstract:

We prove that if A is a C -algebra, then for each a ∈ A , A a = { x ∈ A / x ≤ a } is itself a C -algebra and is isomorphic to the quotient algebra A / θ a of A where θ a = { ( x , y ) ∈ A × A / a ∧ x = a ∧ y } . If A is C -algebra with T , we prove that for every a ∈ B ( A ) , the centre of A , A is isomorphic to A a × A a ′ and that if A is isomorphic A 1 × A 2 , then there exists a ∈ B ( A ) such that A 1 is isomorphic A a and A 2 is isomorphic to A a ′ . Using this decomposition theorem, we prove that if a , b ∈ B ( A ) with a ∧ b = F , then A a is isomorphic to A b if and only if there exists an isomorphism φ on A such that φ ( a ) = b .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:078981

DOI: 10.1155/IJMMS/2006/78981

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