Algebras in varieties of universal algebras

• Grant number: 16/08708-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2016
• End date: October 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Lucio Centrone
• Grantee: Guilherme Vicentin de Toledo
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this master's studies the beneficiary will continue aspects of the research found in the article "Zariski Closed Algebras in Varieties of Universal Algebra" of Belov-Kanel, Giambruno, Rowen and Vishne, concerning the research of Zariski closed algebras representable over an arbitrary integral domain using techniques from the theory of universal algebras.To better explain the concepts involved: an algebra is representable over an integral domain if it is a subalgebra of a finite-dimensional algebra over this domain; the Zariski topology in arbitrary algebras is a generalization of the Zariski topology found in ring theory, where the set of prime ideals of a ring is equipped with a topology where closed sets are those collections of prime ideals containing a given subset of the ring, for each subset of the ring; and universal algebras are generalizations of the structures found in abstract algebra, where the varieties of universal algebras mentioned in the title are classes of such structures satisfying simultaneously arbitrary sets of identities. These studies are a recognition of the growing importance of the topics of universal algebras and algebras with polynomial identities in modern algebra and are consistent with the study area of the advisor; will require of the student an initial approach to universal algebras accompanying the book "A Course in Universal Algebra" by Burris and Sankappanavar, a study of algebras with polynomial identities by the book "Polynomial Identities and Asymptotic Methods" of Giambruno and Zaicev and, as said before, will be deeply based on the cited article. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

TOLEDO, Guilherme Vicentin de. ('jota','ômega')-Algebras and polynomial identities of Zariski-closed representable algebras. 2017. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.