Derivations with invertible values in flexible algebras
Derivations with invertible values of 0 – torsion flexible algebras satisfying x(yz) = (xz)y over an algebraically closed field are described. For this class of algebra with unit element 1 and derivation with invertible value d is either a Cayley – Dickson algebra over its center Z(A) or a factor a...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2019-05-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
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| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/37192 |
| _version_ | 1827767192311037952 |
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| author | Gangireddy Lakshmi Devi K. Jayalakshmi |
| author_facet | Gangireddy Lakshmi Devi K. Jayalakshmi |
| author_sort | Gangireddy Lakshmi Devi |
| collection | DOAJ |
| description |
Derivations with invertible values of 0 – torsion flexible algebras satisfying x(yz) = (xz)y over an algebraically closed field are described. For this class of algebra with unit element 1 and derivation with invertible value d is either a Cayley – Dickson algebra over its center Z(A) or a factor algebra of polynomial algebra C[a]/(a2) over a Cayley – Dickson division algebra; also C is 2 – torsion, d(C) = 0 and d(a) = 1+ua for some u in center of C and d is an outer derivation. Moreover, C is a split Cayley – Dickson algebra over its center Z having a derivation with invertible value d if and only if C is obtained by means of Cayley – Dickson process from its associative division subalgebra and can be represented as a direct sum C = V ⊕ aV.
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| first_indexed | 2024-03-11T11:55:20Z |
| format | Article |
| id | doaj.art-e9ff4e8653cd4ef297243ddcac31d6b3 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:20Z |
| publishDate | 2019-05-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-e9ff4e8653cd4ef297243ddcac31d6b32023-11-08T20:07:18ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-05-0138610.5269/bspm.v38i6.37192Derivations with invertible values in flexible algebrasGangireddy Lakshmi Devi0K. Jayalakshmi1Jawaharlal Nehru Technological University Ananthapur A.P. India.JNTUA College Of Engineering (Anathapuramu) Department of Mathematics Derivations with invertible values of 0 – torsion flexible algebras satisfying x(yz) = (xz)y over an algebraically closed field are described. For this class of algebra with unit element 1 and derivation with invertible value d is either a Cayley – Dickson algebra over its center Z(A) or a factor algebra of polynomial algebra C[a]/(a2) over a Cayley – Dickson division algebra; also C is 2 – torsion, d(C) = 0 and d(a) = 1+ua for some u in center of C and d is an outer derivation. Moreover, C is a split Cayley – Dickson algebra over its center Z having a derivation with invertible value d if and only if C is obtained by means of Cayley – Dickson process from its associative division subalgebra and can be represented as a direct sum C = V ⊕ aV. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/37192Derivationsinvertible valuesflexible algebrasCayley-Dickson algebras |
| spellingShingle | Gangireddy Lakshmi Devi K. Jayalakshmi Derivations with invertible values in flexible algebras Boletim da Sociedade Paranaense de Matemática Derivations invertible values flexible algebras Cayley-Dickson algebras |
| title | Derivations with invertible values in flexible algebras |
| title_full | Derivations with invertible values in flexible algebras |
| title_fullStr | Derivations with invertible values in flexible algebras |
| title_full_unstemmed | Derivations with invertible values in flexible algebras |
| title_short | Derivations with invertible values in flexible algebras |
| title_sort | derivations with invertible values in flexible algebras |
| topic | Derivations invertible values flexible algebras Cayley-Dickson algebras |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/37192 |
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