Units of integral semigroup rings

Wang, Duzhong (1995) Units of integral semigroup rings. Doctoral (PhD) thesis, Memorial University of Newfoundland.

[img] [English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (7Mb)
  • [img] [English] PDF - Accepted Version
    Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
    (Original Version)

Abstract

In this thesis, we study the unit group U(ZS) of the integral semigroup ring ZS of a finite semigroup S. Throughout, we assume that ZS has an identity, and unless mentioned otherwise, it is assumed that QS is a semisimple Artinian ring. -- In the first part, we study large subgroups of U(ZS). First, two types of units are introduced: the Bass cyclic units and the bicyclic units. These are appropriate generalizations of the analogous group ring case. In the main theorem, it is shown that, as in the case of integral group rings, both the Bass cyclic units and bicyclic units generate a subgroup of finite index in U(ZS), for a large class of integral semigroup rings. Because the proof ultimately relies on the celebrated congruence theorems, one has to exclude some semigroups which have some specific Wedderburn simple components of degree 1 or 2 over Q. -- In chapter 3, we deal with some examples. We consider the class of semigroups S that are monoid extensions of elementary Rees semigroups. An algorithm is given to compute generators for the full unit group U(ZS). The algorithm is then applied to a specific example. -- Finally, we classify the semigroups such that the unit group U(ZS) is either finite or has a free subgroup of finite index. The former extends Higman's result to the case of semigroup rings.

Item Type: Thesis (Doctoral (PhD))
URI: http://research.library.mun.ca/id/eprint/746
Item ID: 746
Additional Information: Bibliography: leaves 72-74
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 1995
Date Type: Submission
Library of Congress Subject Heading: Semigroup rings; Unit groups (Ring theory)

Actions (login required)

View Item View Item

Downloads

Downloads per month over the past year

View more statistics