Involutions in group rings and in alternative loop rings

• Grant number: 12/20208-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 07, 2013
• End date: March 06, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francisco Cesar Polcino Milies
• Grantee: Francisco Cesar Polcino Milies
• Visiting researcher: Edgar George Goodaire
• Visiting researcher institution: Memorial University of Newfoundland (MUN), Canada
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Let * denote an involution of a group G. A homomorphism à from G to the set {±1} is called an orientation of G. Let RG denote the group ring of G over a commutative ring R. The map defined in RG by( agg )# = agÃ(g) g*Is called an oriented group involution of RG.We will study commutativity and anti-commutativity of the sets of symmetric and skew-symmetric elements under oriented involutions, and their generalizations, completing joint work done in the past. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GOODAIRE, EDGAR G.; MILIES, CESAR POLCINO. Jordan nilpotency in group rings. Journal of Group Theory, v. 17, n. 4, p. 541-557, JUL 2014. (12/20208-2, 09/52665-0)