On Galois projective group rings
Let A be a ring with 1, C the center of A and G′ an inner automorphism group of A induced by {Uα in A/α in a finite group G whose order is invertible}. Let AG′ be the fixed subring of A under the action of G′.If A is a Galcis extension of AG′ with Galois group G′ and C is the center of the subring...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000145 |
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| _version_ | 1849684037730304000 |
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| author | George Szeto Linjun Ma |
| author_facet | George Szeto Linjun Ma |
| author_sort | George Szeto |
| collection | DOAJ |
| description | Let A be a ring with 1, C the center of A and G′ an
inner automorphism group of A induced by {Uα in A/α in a finite
group G whose order is invertible}. Let AG′ be the fixed subring of
A under the action of G′.If A is a Galcis extension of AG′ with
Galois group G′ and C is the center of the subring ∑αAG′Uα then
A=∑αAG′Uα and the center of AG′ is also C. Moreover, if
∑αAG′Uα is Azumaya over C, then A is a projective group ring. |
| format | Article |
| id | doaj-art-cb63cd2b73464e9386370fd3dbb48348 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cb63cd2b73464e9386370fd3dbb483482025-08-20T03:23:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114114915310.1155/S0161171291000145On Galois projective group ringsGeorge Szeto0Linjun Ma1Mathematics Department, Bradley University, Peoria 61625, Illinois, USAMathematics Department, Zhongshan University, Guangzhou, ChinaLet A be a ring with 1, C the center of A and G′ an inner automorphism group of A induced by {Uα in A/α in a finite group G whose order is invertible}. Let AG′ be the fixed subring of A under the action of G′.If A is a Galcis extension of AG′ with Galois group G′ and C is the center of the subring ∑αAG′Uα then A=∑αAG′Uα and the center of AG′ is also C. Moreover, if ∑αAG′Uα is Azumaya over C, then A is a projective group ring.http://dx.doi.org/10.1155/S0161171291000145central Galois extensionsprojective group ringsAzumaya algebras. |
| spellingShingle | George Szeto Linjun Ma On Galois projective group rings International Journal of Mathematics and Mathematical Sciences central Galois extensions projective group rings Azumaya algebras. |
| title | On Galois projective group rings |
| title_full | On Galois projective group rings |
| title_fullStr | On Galois projective group rings |
| title_full_unstemmed | On Galois projective group rings |
| title_short | On Galois projective group rings |
| title_sort | on galois projective group rings |
| topic | central Galois extensions projective group rings Azumaya algebras. |
| url | http://dx.doi.org/10.1155/S0161171291000145 |
| work_keys_str_mv | AT georgeszeto ongaloisprojectivegrouprings AT linjunma ongaloisprojectivegrouprings |