By Ernest Shult,David Surowski

This e-book offers a graduate-level direction on sleek algebra. it may be used as a instructing publication – due to the copious routines – and as a resource booklet in the event you desire to use the foremost theorems of algebra.

The direction starts with the fundamental combinatorial ideas of algebra: posets, chain stipulations, Galois connections, and dependence theories. the following, the final Jordan–Holder Theorem turns into a theorem on period measures of sure decrease semilattices. this can be by way of easy classes on teams, jewelry and modules; the mathematics of quintessential domain names; fields; the explicit standpoint; and tensor products.

Beginning with introductory strategies and examples, each one bankruptcy proceeds progressively in the direction of its extra advanced theorems. Proofs development step by step from first ideas. Many attention-grabbing effects stay within the routines, for instance, the facts that ideals in a Dedekind area are generated through at so much parts. The emphasis all through is on actual figuring out instead of memorizing a catechism and so a few chapters supply curiosity-driven appendices for the self-motivated student.

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