Advanced Algebra
A.R. Vasishtha
SYLLABUS- ADVANCED ALGEBRA,
Rings: Rings, Various types of rings, Rings with unity, Rings without zero divisors, Properties of rings, Sub rings.
Ideals: Ideals, Quotient rings, Principal ideals, Maximal ideals, Prime ideals, Principal ideal domains, Characteristic of a ring.
Integral Domains and Fields: Integral domain, Field, Skew field etc., Field of quotients of an integral domain, Embedding of an integral domain in a field, Factorization in an integral domain, Divisibility, Units, Associates, Prime and irreducible elements, Unique Factorisation Domain, Euclidean rings.
Polynomial Rings: Polynomials over a ring, Degree of a polynomial, Zero, Constant and monic polynomials, Equality of polynomials, Addition and multiplication of polynomials, Polynomial rings, Embedding of a ring R into R[x], Division algorithm, Euclidean algorithm, Units and associates in polynomials, Irreducible polynomials.
Rings: Rings, Various types of rings, Rings with unity, Rings without zero divisors, Properties of rings, Sub rings.
Ideals: Ideals, Quotient rings, Principal ideals, Maximal ideals, Prime ideals, Principal ideal domains, Characteristic of a ring.
Integral Domains and Fields: Integral domain, Field, Skew field etc., Field of quotients of an integral domain, Embedding of an integral domain in a field, Factorization in an integral domain, Divisibility, Units, Associates, Prime and irreducible elements, Unique Factorisation Domain, Euclidean rings.
Polynomial Rings: Polynomials over a ring, Degree of a polynomial, Zero, Constant and monic polynomials, Equality of polynomials, Addition and multiplication of polynomials, Polynomial rings, Embedding of a ring R into R[x], Division algorithm, Euclidean algorithm, Units and associates in polynomials, Irreducible polynomials.
Категории:
Год:
2018
Язык:
english
Страницы:
144
ISBN:
B095Y9Y7ZV
Файл:
PDF, 1.68 MB
IPFS:
,
english, 2018
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