An Introduction to Gröbner Bases

as Algebra Becomes More Widely Used In A Variety Of Applications And Computers Are Developed To Allow Efficient Calculations In The Field, So There Becomes A Need For New Techniques To Further This Area Of Research. Gröbner Bases Is One Topic Which Has Recently Become A Very Popular And Important Area Of Modern Algebra. This Book Provides A Concrete Introduction To Commutative Algebra Through Gröbner Bases. The Inclusion Of Exercises, Lists Of Further Reading And Related Literature Make This A Practical Approach To Introducing Gröbner Bases. The Author Presents New Concepts And Results Of Recent Research In The Area Allowing Students And Researchers In Technology, Computer Science And Mathematics To Gain A Basic Understanding Of The Technique. A First Course In Algebra Is The Only Prior Knowledge Required For This Introduction. Chapter Titles Include: * Monomial Ldeas * Gröbner Bases * Algebraic Sets * Solving Systems Of Polynomial Equations * Applications Of Gröbner Bases * Homogeneous Algebra * Hilbert Series * Variations Of Gröbner Bases * Improvements To Buchberger's Algorithms * Software booknews a Text For A Course Introducing Commutative Algebra Through Gr bner Bases To Students Of Math, Technology, And Computer Science Who Have Finished A First Course In Algebra Containing Complex Numbers And Some Elementary Linear Algebra. Emphasizes Constructiveness Above Abstraction, Offers Examples For New Concepts And Results, And Keeps The Treatment Elementary In Order To Remain Accessible To A Wide Audience. Annotation C. By Book News, Inc., Portland, Or. As algebra becomes more widely used in a variety of applications and computers are developed to allow efficient calculations int he field, so there becomes a need for new techniques to further this area of research. Gröbner Bases is one topic which has recently become a very popular and important area of modern algebra. This book provides a concrete introduction to commutative algebra through Gröbner Bases. The inclusion of exercises, lists of further reading and related literature make this a practical approach to introducing Gröbner Bases. The author presents new concepts nd results of recent research in the area allowing students and researchers in technology, computer science and mathematics to gain a basic understanding of the technique. A first course in algebra is the only prior knowledge required for this introduction In this chapter we will introduce some basic concepts from commutative algebra that are important for the understanding of the following chapters.