Algebraic structures of the baric algebras, RA loops and linear codes
| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Mem Univ Newfoundland, St John, NF A1C 5S7 - Canada
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05314970 Sao Paulo - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES; v. 56, n. 2, p. 344-353, JUN 2013. |
| Web of Science Citations: | 4 |
| Abstract | |
Let g -> g{*} denote an involution on a group G. For any (commutative, associative) ring R (with 1), {*} extends linearly to an involution of the group ring RG. An element alpha is an element of RG is symmetric if alpha{*} = alpha and skew-symmetric if alpha{*} = alpha. The skew-symmetric elements are closed under the Lie bracket, {[}alpha, beta] = alpha beta - beta alpha. In this paper, we investigate when this set is also closed under the ring product in RG. The symmetric elements are closed under the Jordan product, alpha o beta = alpha beta + beta alpha. Here, we determine when this product is trivial. These two problems are analogues of problems about the skew-symmetric and symmetric elements in group rings that have received a lot of attention. (AU) | |
| FAPESP's process: | 04/15319-3 - Groups and noncommutative algebra: interactions and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 08/57553-3 - Edgar George Goodaire | Memorial University of Newfoundland - Canada |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |