عنوان

Sets and groups :

(Number (ISBN

9401160953

(Number (ISBN

9789401160957

Number

b595934

Title Proper

Sets and groups :

General Material Designation

[Book]

Other Title Information

a first course in algebra

First Statement of Responsibility

by James Alexander Green.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands

Date of Publication, Distribution, etc.

1988

Specific Material Designation and Extent of Item

(xi, 258 pages)

Text of Note

1 Sets --; 1.1 Sets --; 1.2 Subsets --; 1.3 Intersection --; 1.4 Union --; 1.5 The algebra of sets --; 1.6 Difference and complement --; 1.7 Pairs. Product of sets --; 1.8 Sets of sets --; Exercises --; 2 Equivalence relations --; 2.1 Relations on a set --; 2.2 Equivalence relations --; 2.3 Partitions --; 2.4 Equivalence classes --; 2.5 Congruence of integers --; 2.6 Algebra of congruences --; Exercises --; 3 Maps --; 3.1 Maps --; 3.2 Equality of maps --; 3.3 Injective, surjective, bijective maps. Inverse maps. --; 3.4 Product of maps --; 3.5 Identity maps --; 3.6 Products of bijective maps --; 3.7 Permutations --; 3.8 Similar sets --; Exercises --; 4 Groups --; 4.1 Binary operations on a set --; 4.2 Commutative and associative operations --; 4.3 Units and zeros --; 4.4 Gruppoids, semigroups and groups --; 4.5 Examples of groups --; 4.6 Elementary theorems on groups --; Exercises --; 5 Subgroups --; 5.1 Subsets closed to an operation --; 5.2 Subgroups --; 5.3 Subgroup generated by a subset --; 5.4 Cyclic groups --; 5.5 Groups acting on sets --; 5.6 Stabilizers --; Exercises --; 6 Cosets --; 6.1 The quotient sets of a subgroup --; 6.2 Maps of quotient sets --; 6.3 Index. Transversals --; 6.4 Lagrange's theorem --; 6.5 Orbits and stabilizers --; 6.6 Conjugacy classes. Centre of a group --; 6.7 Normal subgroups --; 6.8 Quotient groups --; Exercises --; 7 Homomorphisms --; 7.1 Homomorphisms --; 7.2 Some lemmas on homomorphisms --; 7.3 Isomorphism --; 7.4 Kernel and image --; 7.5 Lattice diagrams --; 7.6 Homomorphisms and subgroups --; 7.7 The second isomorphism theorem --; 7.8 Direct products and direct sums of groups --; Exercises --; 8 Rings and fields --; 8.1 Definition of a ring. Examples --; 8.2 Elementary theorems of rings. Subrings --; 8.3 Integral domains --; 8.4 Fields. Division rings --; 8.5 Polynomials --; 8.6 Homomorphisms. Isomorphism of rings --; 8.7 Ideals --; 8.8 Quotient rings --; 8.9 The Homomorphism Theorem for rings --; 8.10 Principal ideals in a commutative ring --; 8.11 The Division Theorem for polynomials --; 8.12 Polynomials over a field --; 8.13 Divisibility in Z and in F[X] --; 8.14 Euclid's algorithm --; Exercises --; 9 Vector spaces and matrices --; 9.1 Vector spaces over a field --; 9.2 Examples of vector spaces --; 9.3 Two geometric interpretations of vectors --; 9.4 Subspaces --; 9.5 Linear combinations. Spanning sets --; 9.6 Linear dependence. Basis of a vector space --; 9.7 The Basis Theorem. Dimension --; 9.8 Linear maps. Isomorphism of vector spaces --; 9.9 Matrices --; 9.10 Laws of matrix algebra. The ring Mn(F) --; 9.11 Row space of a matrix. Echelon matrices --; 9.12 Systems of linear equations --; 9.13 Matrices and linear maps --; 9.14 Invertible matrices. The group GLn(F) --; Exercises --; Tables --; List of notations --; Answers to exercises.

Science (General)

Class number

Book number

by James Alexander Green.

J A Green

Electronic name

[Book]

Y