UIUC Dept. of Mathematics Seminar Calendar

    February 2011            March 2011             April 2011     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5          1  2  3  4  5                   1  2
  6  7  8  9 10 11 12    6  7  8  9 10 11 12    3  4  5  6  7  8  9
 13 14 15 16 17 18 19   13 14 15 16 17 18 19   10 11 12 13 14 15 16
 20 21 22 23 24 25 26   20 21 22 23 24 25 26   17 18 19 20 21 22 23
 27 28                  27 28 29 30 31         24 25 26 27 28 29 30

Wednesday, March 16, 2011

Algebra, Geometry and Combinatorics Seminar
3:00 pm in 7 Illini Hall, Wednesday, March 16, 2011

Del

Edit

Copy

Submitted by ecsima.

Hamid Kulosman (University of Louisville)
Zero-divisor graphs of some special semigroups
Abstract: We introduce the notion of special semigroups. They are commutative Boolean semigroups that can be built from a trivial semigroup in finitely many steps, where in each step an idempotent is adjoined in one of the three allowed ways. The $i$-th step of the building process is completely described by an element $a_i$ of the set $\{\mathrm{'id'}, \mathrm{'ze'}, 0,1,\dots, i-1 \}$ of $i+2$ elements. The sequence $\mathbf{a}=a_0, a_1,\dots, a_N$, obtained in that way, is called a defining sequence of the semigroup. It follows that the special semigroups form a large class of semigroups each of which can be easily defined. They can be arbitrarily big, nevertheless checking of associativity is completely avoided. Because of that they can be useful for various purposes. We give the description of the zero-divisor graphs of special semigroups and prove various properties of them. This is a joint work with Alica Miller.