Decompositions of a C-algebra
We prove that if A is a C-algebra, then for each a∈A, Aa={x∈A/x≤a} is itself a C-algebra and is isomorphic to the quotient algebra A/θa of A where θa={(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 Aa×Aa′ and that if A is isomorphic...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/78981 |
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| Summary: | We prove that if A is a C-algebra, then for each a∈A, Aa={x∈A/x≤a} is itself a C-algebra and is isomorphic to the quotient algebra A/θa of A where θa={(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 Aa×Aa′ and that if A is isomorphic A1×A2, then there exists a∈B(A) such that A1 is isomorphic Aa and A2 is isomorphic to Aa′. Using this decomposition theorem, we prove that if a,b∈B(A) with a∧b=F, then Aa is isomorphic to Ab if and only if there exists an isomorphism φ on A such that φ(a)=b. |
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| ISSN: | 0161-1712 1687-0425 |