ALGEBRA SEMINAR

Current seminar: Monday, January 15th, 14:00 - 15:00, the seminar room of KA (319/334)

Yuriy Ishchuk (Univ. of Lviv):
THE ZERO-DIVISORS GRAPHS OF FINITE RINGS AND MATRIX SEMIGROUPS

Abstract: A commutative ring R can be considered as a simple graph whose vertices are elements of R and two different elements x and y of R are adjacent if and only if xy=0. The idea of colouring of a commutative ring establishes a connection between graph theory and commutative ring theory which hopefully will turn out to be mutually beneficial for these two branches of mathematics. In a manner analogous to the commutative case, the zero-divisor graph of a non-commutative semigroup S can be defined as the directed graph \Gamma(S) whose vertices are all non-zero zero-divisors of S$ in which for any two distinct vertices x and y, x\to y is an edge if and only if xy=0. In the talk, we shall discuss the interplay between the properties of a matrix semigroup S over a finite ring R and the graph-theoretic properties of \Gamma(S), \Gamma(R): the connectedness, diameter, existence of sources, sinks, etc.

Forthcoming:

February 19th - Jan Šťovíček (MFF UK): FLAT EPIMORPHISMS FOR COMMUTATIVE NOETHERIAN RINGS

February 26th - Roger Wiegand (Univ. Nebraska): BETTI TABLES OVER SHORT GORENSTEIN ALGEBRAS

Previous program: 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 1997-2002.


The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.

Presently, the seminar is supported by ECI and GACR. It serves primarily as a platform for presentation of recent research of the visitors to the ECI and to the Department of Algebra, as well as members of the Department and their students.