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McCoy N.H. — The theory of rings
McCoy N.H. — The theory of rings

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Название: The theory of rings

Автор: McCoy N.H.


The theory of rings is not only important in mathematics but in also in applications of algebra, such as cryptography, coding theory, and theoretical physics. The theory of rings has advanced considerably since this book was published, but the book emphasizes the fundamentals, which have not changed, and so could still be used as an introduction to these modern developments. The book is written for undergraduates who have had prior exposure to modern algebra.There are many exercises at the end of each chapter, and hints of some of their solutions in the back of the book. Ring theory used to be viewed as an abstract, esoteric subject, but this attitude has changed due to its many applications. Commutative rings are the emphasis in the book, and this reflects somewhat its time of publication. Noncommutative rings have been the subject of intense investigation in the last decade, going by the name of quantum algebra. Quantum algebra has its origins in theory of exactly solved models in statistical mechanics, but has now established itself as a rigorous subfield of modern algebra. Readers interested in this area of research will be well prepared after a study of this book. Some of the highlights of the book, a few of which are usually not included in a beginning course in ring theory include the discussions on ideals in complete metric rings, dense rings, and modular ideals.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 166

Добавлена в каталог: 30.10.2010

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Предметный указатель
Addition      1
Addition of ideals      27
Addition of subspaces      92
Additive group of a ring      2
Additive inverse      1
Algebra      10
Algebra of matrices      11
Algebra of quaternions      14
Annihilating right ideal      100
Annihilating subspace      100
Anti-isomorphism      83 101
Ascending chain condition (A.C.C.)      36
Associative laws      1 2
Basis of a vector space      92
Basis of an ideal      28
Boolean ring      10
Center      8
centralizer      90
Characteristic      4
Commutative law      1
Commutative ring      2
Complete direct sum      19 50
Complete matrix ring      14
Component rings of direct sum      18
Dense ring      95
Descending chain condition (d.c.c.)      35
Difference group      41
Dimension of vector space      93
Direct sum of rings      18
Direct sum of rings of ideals      28
Discrete direct sum      19 50
Distributive laws      2
Division ring      6
Divisor of zero      4
Endomorphism      75
Faithful representation      147
Field      6
Fundamental theorem on homomorphisms      45
G-regular      132
Group algebra      12
Homomorphism      43
Ideal      21
Ideal, generated by a set      23
Idempotent element      5
Image space      94
Integral domain      5
Inverse      5
Irreducible R-module      148
Irreducible ring of endomorphisms      82
Isomorphism      6
Jacobson radical      112
Join of ideals      27 28
Kernel of homomorphism      44
Largest nil ideal      33
Left ideal      21
Left inverse      5
Left multiplication      84
Left unity      2
Linear transformation      94
Lower radical      146
m-system      63
Matrix units      14
Maximal ideal      34
Minimal ideal      34
Minimum condition      142
Modular ideal      134
Modular law      142
Modular right ideal      88
Multiplication      1
Multiplication of ideals      31
Multiplicative system      64
n-system      67
Natural homomorphism      45 52
Nil ideal      31
Nilpotent element      4
Nilpotent ideal      31
Noncommutative ring      2
Nonzero ring      2
Norm of a quaternion      19
Null space      94
p-ring      61
Partially ordered set      140
Prime ideal      62
Prime radical of a ring      69
Prime radical of an ideal      64
Prime ring      71
Primitive ring      83
Principal ideal      23
Product of ideals      31
Projection      122
Quasi-inverse      111
Quasi-regular      111
Quaternions      13
R-endomorphism      90
R-isomorphism      49 89
R-module      84
R-subgroup      82
Radical $\mathfrak{R}(R)$      132
Regular element      123
Regular ring      123
Representation      52 147
Residue-class ring      41
Right ideal      21
Right inverse      5
Right multiplication      80
Right unity      2
Ring      1
Ring of extended power series      17
Ring of formal power series      15
Ring of matrices      7 11
Ring of subsets of a set      7
Scalar matrix      15
Semi-prime ideal      66
Semi-prime ring      146
Simple ring      38
Socle      143
Subdirect sum      52
Subdirectly irreducible ring      55
Subring      2
UNIT      5
Unity      2
Vector space      91
Wedderburn — Artin theorem      106
Zero of a ring      1
Zorn's lemma      54 144
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