Tiled orders, exponent matrixes, units in rings and related topics

• Grant number: 15/16726-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: November 01, 2015
• End date: January 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Mikhailo Dokuchaev
• Visiting researcher: Volodymyr Kyrychenko
• Visiting researcher institution: Taras Shevchenko National University of Kyiv, Ukraine
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 15/09162-9 - Non commutative algebra and applications, AP.TEM

Abstract

The project will be dedicated to the study of exponent matrixes of tiled orders, relations of tiled orders to other classes of semi-perfect rings and some aspects on groups of units in rings. More precisely, we will consider the problem of the classification of exponent matrixes, mainly via study of minimal non-negative exponent matrixes, with special attention payed to (0,1)-matrixes. We shall also investigate the relation between tiled orders and other relevant classes of rings such as semi-perfect semi-distributive rings, serial rings, Gorenstein rings and quasi-Frobenius rings. We will also consider groups of invertible elements in tiled rings, serial rings and other classes of semi-perfect rings. (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)

DOKUCHAEV, MIKHAILO; KIRICHENKO, VLADIMIR; KUDRYAVTSEVA, GANNA; PLAKHOTNYK, MAKAR. The max-plus algebra of exponent matrices of tiled orders. Journal of Algebra, v. 490, p. 1-20, NOV 15 2017. (15/09162-9, 13/11350-2, 15/16726-6, 14/23853-1)