integral domain


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integral domain

[′int·ə·grəl dō′mān]
(mathematics)
A commutative ring with identity where the product of nonzero elements is never zero. Also known as entire ring.
References in periodicals archive ?
This is followed by a range of current topics such as multilinear algebra, matrix polynomials and equations, perturbation theory, pseudospectra, inverse problems, integral domains, and spectral sets, among many others.
Simple extensions with the minimum degree relations of integral domains.
Among the topics are greatest common divisors, integer multiples and exponents, quotients of polynomial rings, divisibility and factorization in integral domains, subgroups of cyclic groups, cosets and Lagrange's theorem, the fundamental theorem of finite abelian groups, and check digits.
Nicholson starts with a review of proofs, sets, mappings and equivalences, then in 11 chapters covers integers and permutations, groups, rings, polynomials, factorization in integral domains, fields, modules over principal ideal domains, p-groups and the Sylow theorems, series of subgroups, Galois theory and finiteness conditions for rings and modules.

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