This e-book surveys greater than a hundred twenty five years of facets of associative algebras, particularly ring and module conception. it's the first to probe so greatly this type of wealth of old improvement. additionally, the writer brings the reader modern, particularly via his document at the topic within the moment half the 20 th century. incorporated within the ebook are yes specific houses from theorems of Frobenius and Stickelberger at the fundamental decomposition of finite Abelian teams; Hilbert's foundation theorem and his Nullstellensatz, together with the fashionable formulations of the latter through Krull, Goldman, and others; Maschke's theorem at the illustration idea of finite teams over a box; and the basic theorems of Wedderburn at the constitution of finite dimensional algebras and finite skew fields and their extensions through Braver, Kaplansky, Chevalley, Goldie, and others. a unique characteristic of the e-book is the in-depth examine of jewelry with chain situation on annihilator beliefs pioneered by way of Noether, Artin, and Jacobson and subtle and prolonged via many later mathematicians. of the author's earlier works, Algebra: jewelry, Modules and different types, I and II (Springer-Verlag, 1973), are dedicated to the advance of contemporary associative algebra and ring and module conception. these works function a beginning for the current survey, which incorporates a bibliography of over 1,600 references and is exhaustively listed. as well as the mathematical survey, the writer provides candid and descriptive impressions of the final 1/2 the 20th century in ``Part II: Snapshots of a few Mathematical buddies and Places''. starting along with his lecturers and fellow graduate scholars on the college of Kentucky and at Purdue, religion discusses his Fulbright-NATO Postdoctoral at Heidelberg and on the Institute for complicated examine (IAS) at Princeton, his yr as a vacationing student at Berkeley, and the various neighbors he met there and in next travels in India, Europe, and so much lately, Barcelona. reviews at the first version: ``Researchers in algebra should still locate it either stress-free to learn and extremely valuable of their paintings. In all circumstances, [Faith] cites complete references as to the starting place and improvement of the theory .... i do know of no different paintings in print which does this as completely and as broadly.'' --John O'Neill, college of Detroit at Mercy `` `Part II: Snapshots of a few Mathematical acquaintances and locations' is exceptional! [It is] a pleasure to learn! Mathematicians of my age and more youthful will enjoy analyzing `Snapshots'.'' --James A. Huckaba, collage of Missouri-Columbia

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