Introduction to groups rings and fields ht and tt 2011 h a priestley 0 familiar algebraic systems review and a look ahead grf is an algebra course and specifically a course about algebraic structures. Rings fields and groups gives a stimulating and unusual introduction to the results methods and ideas now commonly studied on abstract algebra courses at undergraduate level. Abstract algebra deals with three kinds of object groups rings and fields a group is defined as a set of elements together with an operation performed on pairs of these elements such that the operation when given two elements of the set as arguments always returns an element of the set as its result. Groups rings and fields karl heinz fieseler uppsala 2010 1 preface these notes give an introduction to the basic notions of abstract algebra groups rings so far as they are necessary for the construction of eld exten sions and galois theory each section is followed by a series of problems 1 introduction 4 2 groups 12
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