MINIMAL VARIETIES AND IDENTITIES OF RELATIVELY FREE ALGEBRAS

Author(s)

Goncalves, Dimas Jose ^[1] ; de Mello, Thiago Castilho ^[2]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13560 Sao Carlos, SP - Brazil

^[2] Univ Fed Sao Paulo, Inst Ciencia & Tecnol, BR-12231280 Sao Jose Dos Campos - Brazil

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 43, n. 12, p. 5217-5235, 2015.
• Web of Science Citations: 0

Abstract

Let K be a field of characteristic zero and let R-5 be the variety of associative algebras over K, defined by the identity {[}x(1), x(2)]{[}x(3), x(4), x(5)]. It is well-known that such variety is a minimal variety and that it is generated by the algebra Lambda = {[}GRAPHICS] where E = E-0 circle plus E-1 is the Grassmann algebra. In this article, for any positive integer k, we describe the polynomial identities of the relatively free algebras of rank k of R-5, F-k(R-5) = K < x(1), ..., x(k)> /K < x(1), ..., x(k)> boolean AND T(R-5) It turns out that such algebras satisfy the same polynomial identities of some algebras used in the description of the subvarieties of R-5, given by Di Vincenzo, Drensky, and Nardozza. (AU)

• FAPESP's process: 12/16838-0 - Basic superrank and subvarieties of T-prime algebras.
• Grantee: Thiago Castilho de Mello
• Support Opportunities: Scholarships in Brazil - Post-Doctoral