GATE (Graduate Aptitude Test in Engineering) Computer Science & IT (CS) Set Theory & Algebra-Groups Study Material (Page 6 of 8)

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Integral Domains

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Integral Domains

  • In algebra, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility. In an integral domain, every nonzero element a has the cancellation property, that is, if , an equality

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Fields

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Fields

It is a set on which addition, subtraction, multiplication, and division are defined, and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics.

Alternatively, a field is any…

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