Download Dictionary of Algebra, Arithmetic, and Trigonometry by Steven G. Krantz PDF

By Steven G. Krantz

Transparent, rigorous definitions of mathematical phrases are the most important to solid clinical and technical writing-and to figuring out the writings of others. Scientists, engineers, mathematicians, economists, technical writers, machine programmers, besides lecturers, professors, and scholars, all have the necessity for understandable, operating definitions of mathematical expressions. to fulfill that want, CRC Press proudly introduces its Dictionary of Algebra, mathematics, and Trigonometry- the second one released quantity within the CRC accomplished Dictionary of arithmetic. greater than 3 years in improvement, best lecturers and execs from prestigious associations around the globe deliver you greater than 2,800 targeted definitions, written in a transparent, readable kind, entire with substitute meanings, and similar references.From Abelian cohomology to 0 ring and from the very uncomplicated to the hugely complicated, this targeted lexicon comprises phrases linked to mathematics, algebra, and trigonometry, with average overlap into geometry, topology, and different comparable areas.Accessible but rigorous, concise yet finished, the Dictionary of Algebra, mathematics, and Trigonometry is your key to accuracy in writing or knowing clinical, engineering, and mathematical literature.

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Bravais class An arithmetic crystal class determined by (L, B(L)), where L is a lattice and B(L) is the Bravis group of L. See Bravais group. bounded torsion group A torsion group T where there is an integer n ≥ 0 such that t n = 1 for all t ∈ T . Bravais group The group of all orthogonal transformations that leave invariant a given lattice L. c 2001 by CRC Press LLC Bravais lattice A representative of a Bravais type. See Bravais type. Bravais type An equivalence class of arithmetically equivalent lattices.

K). canonical homomorphism (1) Let R be a commutative ring with identity and let L, M be algebras over R. Then, the tensor product L ⊗R M of R-modules is an algebra over R. The mappings l → l ⊗ 1 (l ∈ L) and m → m ⊗ 1 (m ∈ M) give algebra homorphisms L → L ⊗R M and M → L ⊗R M. Each one of these homomorphisms is called a canonical homomorphism (on tensor products of algebras). (2) Let the ring R = i∈I Ri be the direct product of rings Ri . The mapping φi : R → Ri that assigns to each element r of R its ith component ri is called a canonical homomorphism (of direct product of rings).

See Lie group. complex multiplication (1) The multiplication of two complex numbers a + ib and c + id (where a, b, c, d are real) using the rule (a + ib)(c + id) = (ac − bd) + i(ad + bc) , which is simply the usual rule for multiplying binomials, coupled with the property that i 2 = −1. (2) The multiplication of two complexes of a group, which is defined as follows. , subsets of G. Then AB = {ab : a ∈ A, b ∈ B}. , A(BC) = (AB)C for all complexes A, B, C of G. complex number A number of the form z = x + iy where x and y are real and i 2 = −1.

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