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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| Format: | Article |
| Language: | English |
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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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| author | G. C. Rao P. Sundarayya |
| author_facet | G. C. Rao P. Sundarayya |
| author_sort | G. C. Rao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fb4655eeb0894a8ea139748d91f82ef8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fb4655eeb0894a8ea139748d91f82ef82025-02-03T06:48:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/7898178981Decompositions of a C-algebraG. C. Rao0P. Sundarayya1Department of Mathematics, Andhra University, Visakhapatnam 530 003, IndiaDepartment of Mathematics, Andhra University, Visakhapatnam 530 003, IndiaWe 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.http://dx.doi.org/10.1155/IJMMS/2006/78981 |
| spellingShingle | G. C. Rao P. Sundarayya Decompositions of a C-algebra International Journal of Mathematics and Mathematical Sciences |
| title | Decompositions of a C-algebra |
| title_full | Decompositions of a C-algebra |
| title_fullStr | Decompositions of a C-algebra |
| title_full_unstemmed | Decompositions of a C-algebra |
| title_short | Decompositions of a C-algebra |
| title_sort | decompositions of a c algebra |
| url | http://dx.doi.org/10.1155/IJMMS/2006/78981 |
| work_keys_str_mv | AT gcrao decompositionsofacalgebra AT psundarayya decompositionsofacalgebra |