6 research outputs found
On monomial Burnside rings
Cataloged from PDF version of article.This thesis is concerned with some different aspects of the monomial Burnside
rings, including an extensive, self contained introduction of the A−fibred G−sets,
and the monomial Burnside rings. However, this work has two main subjects that
are studied in chapters 6 and 7.
There are certain important maps studied by Yoshida in [16] which are very
helpful in understanding the structure of the Burnside rings and their unit groups.
In chapter 6, we extend these maps to the monomial Burnside rings and find the
images of the primitive idempotents of the monomial Burnside C−algebras. For
two of these maps, the images of the primitive idempotents appear for the first
time in this work.
In chapter 7, developing a line of research persued by Dress [9], Boltje [6],
Barker [1], we study the prime ideals of monomial Burnside rings, and the primitive
idempotents of monomial Burnside algebras. The new results include;
(a): If A is a π−group, then the primitive idempotents of Z(π)B(A, G) and
Z(Ï€)B(G) are the same
(b): If G is a π
0−group, then the primitive idempotents of Z(π)B(A, G) and
QB(A, G) are the same
(c): If G is a nilpotent group, then there is a bijection between the primitive
idempotents of Z(Ï€)B(A, G) and the primitive idempotents of QB(A, K) where
K is the unique Hall π
0−subgroup of G.
(Z(π) = {a/b ∈ Q : b /∈ ∪p∈πpZ}, π =a set of prime numbers).Yaraneri, ErgünM.S
Inductions, restrictions, evaluations, and sunfunctors of Mackey functors
Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 178-179.Yaraneri, ErgünPh.D
Intersection Graph of a Module
Let be a left -module where is a (not necessarily commutative)
ring with unit. The intersection graph \cG(V) of proper -submodules of
is an undirected graph without loops and multiple edges defined as follows: the
vertex set is the set of all proper -submodules of and there is an edge
between two distinct vertices and if and only if We
study these graphs to relate the combinatorial properties of \cG(V) to the
algebraic properties of the -module We study connectedness, domination,
finiteness, coloring, and planarity for \cG (V). For instance, we find the
domination number of \cG (V). We also find the chromatic number of \cG(V)
in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs
in \cG (V) determining the structure of for which \cG(V) is planar