Titlebook: Algebra; A Teaching and Sourc Ernest Shult,David Surowski Textbook 2015 Springer International Publishing Switzerland 2015 Fields.Groups Ri

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Susan C. Levine,Marie T. Banich,Hongkeun Kimof the ring. Many examples of rings are presented—for example the monoid rings (which include group rings and polynomial rings of various kinds), matrix rings, quaternions, algebraic integers etc. This menagerie of rings provides a playground in which the student can explore the basic concepts (idea

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Yoshiomi Nakagami,Masamichi Takesakid a field and is shipped off to Chap.?.. For the domains . which remain, divisibility is a central question. A prime ideal has the property that elements outside the ideal are closed under multiplication. A non-zero element . is said to be . if the principle ideal . which it generates is a prime ide

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Duality for Quasi-convex Supremization,assified in this chapter. They are uniquely determined by a collection of ring elements called the .. This theory is applied to two of the most prominent PIDs in mathematics: the ring of integers, ., and the polynomial rings .[.], where . is a field. In the case of the integers, the theory yields a

Contracture

https://doi.org/10.1007/0-387-28395-1 a . extension of .. The element . is . over . if . is finite. Field theory is largely a study of field extensions. A central theme of this chapter is the exposition of Galois theory, which concerns a correspondence between the poset of intermediate fields of a finite normal separable extension . an

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Ernest Shult,David SurowskiPresents an accessible avenue to the major theorems of modern algebra.Each chapter can be easily adapted to create a one-semester course.Written in a lively, engaging style.Includes supplementary mate

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