Download PDF by Dinh V. Huynh, S. K. Jain, and S. R. López-Permouth: Algebra and Its Applications

By Dinh V. Huynh, S. K. Jain, and S. R. López-Permouth

ISBN-10: 0821838423

ISBN-13: 9780821838426

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ISBN-13: 9781719713696

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This quantity comprises contributions via audio system at a convention on Algebra and Its purposes that happened in Athens, Ohio, in March of 2005. It offers a image of the range of subject matters and purposes that curiosity algebraists this day. The papers during this quantity comprise a few of the most modern leads to the speculation of modules, noncommutative earrings, illustration concept, matrix conception, linear algebra over noncommutative earrings, cryptography, error-correcting codes over finite earrings, and projective-geometry codes, in addition to expository articles that might offer algebraists and different mathematicians, together with graduate scholars, with an obtainable creation to parts outdoors their very own services. The booklet will serve either the professional trying to find the most recent outcome and the amateur looking an available reference for many of the rules and effects awarded the following

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10. 9B COROLLARY (FROBENIUS AND STICKELBERGER [1878]). Any finite Abelian group is a direct sum of cyclic groups of prime power orders. This theorem generalizes the fundamental theorem (FTAG) in one respect: A need not be finitely generated to be of bounded order. 10. Divisible Groups. An Abelian group A is divisible provided that nA = A for any integer n ^ 0. The field Q of rational numbers under addition is an example, and so is any vector space over Q. Another example is Q/Z the factor group of Q modulo Z.

If / is a finite set, say 7 = { l , . . , n } , then the direct sum and direct product coincide, and M = Mx 0 • • • 0 Mn = M1 x • • • x Mn denotes both © ^ = 1 M{ and l\™=1 M*. M is then said to be the internal direct sum of the family { M / } ^ / of submodules: Notation: M = M{ 0 • • • 0 M ; and the modules M[ are summands, Vi. -modules, Hom/^M, N) denotes the set of all mappings ( = homomorphisms) / : M —> TV. It is an Abelian group under pointwise additions of mappings. Further, EndMtf = Hom i?

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Algebra and Its Applications by Dinh V. Huynh, S. K. Jain, and S. R. López-Permouth

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