域论（第2版）
目 录内容简介
preface
contents
0 preliminaries
0.1 lattices
0.2 groups
0.3 the symmetric group
0.4 rings
0.5 integral domains
0.6 unique factorization domains
0.7 principal ideal domains
查看完整
contents
0 preliminaries
0.1 lattices
0.2 groups
0.3 the symmetric group
0.4 rings
0.5 integral domains
0.6 unique factorization domains
0.7 principal ideal domains
查看完整
目 录内容简介
《普通高等教育“十二五”规划教材：聚合物复合材料（第2版）》为高分子材料科学与工程本科以上专业教材之一。聚合物复合材料是一门内容广阔、与其他许多学科交叉渗透、相互关联的综合性学科。它是以聚合物为基体，与各种增强材料和填充材料复合而成的多组分、多相的体系，具有优异的力学性能以及其他性能。所以在许多领域已获得广泛应用。
《普通高等教育“十二五”规划教材：聚合物复合材料（第2版）》是在2001版的《聚合物复合材料》教材的基础进行修订的。2001版教材通过10年的教学使用，得到普遍好评，并多次再版。随着科学技术的发展，本书第二版也在第一版的基础上对部分内容进行了更新，引进了反映当代新研究水平的内容，使学生在掌握基础理论的同时，了解课程的新研究成果和动向，以适应教学改革的需要。本书还对第一版的内容进行了精炼与修正，使本教材更能适应现代科学发展的需要，培养出聚合物复合材料发展前沿的高水平人才。
《普通高等教育“十二五”规划教材：聚合物复合材料（第2版）》是在2001版的《聚合物复合材料》教材的基础进行修订的。2001版教材通过10年的教学使用，得到普遍好评，并多次再版。随着科学技术的发展，本书第二版也在第一版的基础上对部分内容进行了更新，引进了反映当代新研究水平的内容，使学生在掌握基础理论的同时，了解课程的新研究成果和动向，以适应教学改革的需要。本书还对第一版的内容进行了精炼与修正，使本教材更能适应现代科学发展的需要，培养出聚合物复合材料发展前沿的高水平人才。
目 录内容简介
preface
contents
0 preliminaries
0.1 lattices
0.2 groups
0.3 the symmetric group
0.4 rings
0.5 integral domains
0.6 unique factorization domains
0.7 principal ideal domains
0.8 euclidean domains
0.9 tensor products
exercises
part i-field extensions
1 polynomials
1.1 polynomials over a ring
1.2 primitive polynomials and irreducibility
1.3 the division algorithm and its consequences
1.4 splitting fields
.1.5 the minimal polynomial
1.6 multiple roots
1.7 testing for irreducibility
exercises
2 field extensions
2.1 the lattice of subfields of a field
2.2 types of field extensions
2.3 finitely generated extensions
2.4 simple extensions
2.5 finite extensions
2.6 algebraic extensions
2.7 algebraic closures
2.8 embeddings and their extensions.
2.9 splitting fields and normal extensions
exercises
3 embeddings and separability
3.1 recap and a useful lemma
3.2 the number of extensions: separable degree
3.3 separable extensions
3.4 perfect fields
3.5 pure inseparability
3.6 separable and purely inseparable closures
exercises
4 algebraic independence
4.1 dependence relations
4.2 algebraic dependence
4.3 transcendence bases
4.4 simple transcendental extensions
exercises
part ii——-galois theory
5 galois theory i: an historical perspective
5.1 the quadratic equation
5.2 the cubic and quartic equations
5.3 higher-degree equations
5.4 newton's contribution: symmetric polynomials
5.5 vandermonde
5.6 lagrange
5.7 gauss
5.8 back to lagrange
5.9 galois
5.10 a very brief look at the life of galois
6 galois theory i1: the theory
6.1 galois connections
6.2 the galois correspondence
6.3 who's closed?
6.4 normal subgroups and normal extensions
6.5 more on galois groups
6.6 abelian and cyclic extensions
*6.7 linear disjointness
exercises
7 galois theory iii: the galois group of a polynomial
7.1 the galois group of a polynomial
7.2 symmetric polynomials
7.3 the fundamental theorem of algebra.
7.4 the discriminant of a polynomial
7.5 the galois groups of some small-degree polynomials
exercises
8 a field extension as a vector space
8.1 the norm and the trace
*8.2 characterizing bases
*8.3 the normal basis theorem
exercises
9 finite fields i: basic properties
9.1 finite fields redux
9.2 finite fields as splitting fields
9.3 the subfields of a finite field.
9.4 the multiplicative structure of a finite field
9.5 the galois group of a finite field
9.6 irreducible polynomials over finite fields
*9.7 normal bases
*9.8 the algebraic closure of a finite field
exercises
10 finite fields i1: additional properties
10.1 finite field arithmetic
10.2 the number of irreducible polynomials
10.3 polynomial functions
10.4 linearized polynomials
exercises
11 the roots of unity
11.1 roots of unity
11.2 cyclotomic extensions
11.3 normal bases and roots of unity
11.4 wedderburn's theorem
11.5 realizing groups as galois groups
exercises
12 cyclic extensions
12.1 cyclic extensions
12.2 extensions of degree char（f）
exercises
13 solvable extensions
13.1 solvable groups
13.2 solvable extensions
13.3 radical extensions
13.4 solvability by radicals
13.5 solvable equivalent to solvable by radicals
13.6 natural and accessory irrationalities
13.7 polynomial equations
exercises
part iii——the theory of binomials
14 binomials
14.1 irreducibility
14.2 the galois group of a binomial
14.3 the independence of irrational numbers
exercises
15 families of binomials
15.1 the splitting field
15.2 dual groups and pairings
15.3 kummer theory
exercises
appendix: mobius inversion
partially ordered sets
the incidence algebra of a partially ordered set
classical mobius inversion
multiplicative version of m6bius inversion
references
index
^ 收 起
contents
0 preliminaries
0.1 lattices
0.2 groups
0.3 the symmetric group
0.4 rings
0.5 integral domains
0.6 unique factorization domains
0.7 principal ideal domains
0.8 euclidean domains
0.9 tensor products
exercises
part i-field extensions
1 polynomials
1.1 polynomials over a ring
1.2 primitive polynomials and irreducibility
1.3 the division algorithm and its consequences
1.4 splitting fields
.1.5 the minimal polynomial
1.6 multiple roots
1.7 testing for irreducibility
exercises
2 field extensions
2.1 the lattice of subfields of a field
2.2 types of field extensions
2.3 finitely generated extensions
2.4 simple extensions
2.5 finite extensions
2.6 algebraic extensions
2.7 algebraic closures
2.8 embeddings and their extensions.
2.9 splitting fields and normal extensions
exercises
3 embeddings and separability
3.1 recap and a useful lemma
3.2 the number of extensions: separable degree
3.3 separable extensions
3.4 perfect fields
3.5 pure inseparability
3.6 separable and purely inseparable closures
exercises
4 algebraic independence
4.1 dependence relations
4.2 algebraic dependence
4.3 transcendence bases
4.4 simple transcendental extensions
exercises
part ii——-galois theory
5 galois theory i: an historical perspective
5.1 the quadratic equation
5.2 the cubic and quartic equations
5.3 higher-degree equations
5.4 newton's contribution: symmetric polynomials
5.5 vandermonde
5.6 lagrange
5.7 gauss
5.8 back to lagrange
5.9 galois
5.10 a very brief look at the life of galois
6 galois theory i1: the theory
6.1 galois connections
6.2 the galois correspondence
6.3 who's closed?
6.4 normal subgroups and normal extensions
6.5 more on galois groups
6.6 abelian and cyclic extensions
*6.7 linear disjointness
exercises
7 galois theory iii: the galois group of a polynomial
7.1 the galois group of a polynomial
7.2 symmetric polynomials
7.3 the fundamental theorem of algebra.
7.4 the discriminant of a polynomial
7.5 the galois groups of some small-degree polynomials
exercises
8 a field extension as a vector space
8.1 the norm and the trace
*8.2 characterizing bases
*8.3 the normal basis theorem
exercises
9 finite fields i: basic properties
9.1 finite fields redux
9.2 finite fields as splitting fields
9.3 the subfields of a finite field.
9.4 the multiplicative structure of a finite field
9.5 the galois group of a finite field
9.6 irreducible polynomials over finite fields
*9.7 normal bases
*9.8 the algebraic closure of a finite field
exercises
10 finite fields i1: additional properties
10.1 finite field arithmetic
10.2 the number of irreducible polynomials
10.3 polynomial functions
10.4 linearized polynomials
exercises
11 the roots of unity
11.1 roots of unity
11.2 cyclotomic extensions
11.3 normal bases and roots of unity
11.4 wedderburn's theorem
11.5 realizing groups as galois groups
exercises
12 cyclic extensions
12.1 cyclic extensions
12.2 extensions of degree char（f）
exercises
13 solvable extensions
13.1 solvable groups
13.2 solvable extensions
13.3 radical extensions
13.4 solvability by radicals
13.5 solvable equivalent to solvable by radicals
13.6 natural and accessory irrationalities
13.7 polynomial equations
exercises
part iii——the theory of binomials
14 binomials
14.1 irreducibility
14.2 the galois group of a binomial
14.3 the independence of irrational numbers
exercises
15 families of binomials
15.1 the splitting field
15.2 dual groups and pairings
15.3 kummer theory
exercises
appendix: mobius inversion
partially ordered sets
the incidence algebra of a partially ordered set
classical mobius inversion
multiplicative version of m6bius inversion
references
index
^ 收 起
目 录内容简介
《普通高等教育“十二五”规划教材：聚合物复合材料（第2版）》为高分子材料科学与工程本科以上专业教材之一。聚合物复合材料是一门内容广阔、与其他许多学科交叉渗透、相互关联的综合性学科。它是以聚合物为基体，与各种增强材料和填充材料复合而成的多组分、多相的体系，具有优异的力学性能以及其他性能。所以在许多领域已获得广泛应用。
《普通高等教育“十二五”规划教材：聚合物复合材料（第2版）》是在2001版的《聚合物复合材料》教材的基础进行修订的。2001版教材通过10年的教学使用，得到普遍好评，并多次再版。随着科学技术的发展，本书第二版也在第一版的基础上对部分内容进行了更新，引进了反映当代新研究水平的内容，使学生在掌握基础理论的同时，了解课程的新研究成果和动向，以适应教学改革的需要。本书还对第一版的内容进行了精炼与修正，使本教材更能适应现代科学发展的需要，培养出聚合物复合材料发展前沿的高水平人才。
《普通高等教育“十二五”规划教材：聚合物复合材料（第2版）》是在2001版的《聚合物复合材料》教材的基础进行修订的。2001版教材通过10年的教学使用，得到普遍好评，并多次再版。随着科学技术的发展，本书第二版也在第一版的基础上对部分内容进行了更新，引进了反映当代新研究水平的内容，使学生在掌握基础理论的同时，了解课程的新研究成果和动向，以适应教学改革的需要。本书还对第一版的内容进行了精炼与修正，使本教材更能适应现代科学发展的需要，培养出聚合物复合材料发展前沿的高水平人才。
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