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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)

Articles published in Agência FAPESP Newsletter about the research grant:
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Articles published in other media outlets ( ):
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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, . (15/09162-9, 13/11350-2, 15/16726-6, 14/23853-1)