Commutative algebra: constructive methods - finite projective modules
Lombardi, Henri
Commutative algebra: constructive methods - finite projective modules - Dordrecht: Springer, 2015 - xlix, 996p. pb; 24 cm - Algebra and applications, 1572-5553; Vol.20 .
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors, and theoretical computer scientists.
9789402403992
Field Theory and Polynomials.
MATHEMATICS -- Intermediate
Symbolic and Algebraic Manipulation.
Algebra
Mathematics
Computer science -- Mathematics
Commutative Rings.
Commutative Algebra.
Commutative Rings and Algebras.
Linear and Multilinear Algebras, Matrix Theory.
Matrix theory.
Field theory (Physics)
Algebra
512.44 LOM
Commutative algebra: constructive methods - finite projective modules - Dordrecht: Springer, 2015 - xlix, 996p. pb; 24 cm - Algebra and applications, 1572-5553; Vol.20 .
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors, and theoretical computer scientists.
9789402403992
Field Theory and Polynomials.
MATHEMATICS -- Intermediate
Symbolic and Algebraic Manipulation.
Algebra
Mathematics
Computer science -- Mathematics
Commutative Rings.
Commutative Algebra.
Commutative Rings and Algebras.
Linear and Multilinear Algebras, Matrix Theory.
Matrix theory.
Field theory (Physics)
Algebra
512.44 LOM
