Introduction to Ring Theory (Springer Undergraduate Mathematics Series)
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Publication Date:. Number of Pages:. The book under review consists of two parts and the prerequisites.
The prerequisites cover primarily some basic Set Theory and can be skipped by a reader already familiar with the notions; however, this section is important to keep the book self-contained. The two parts are very different by their content, style, and purpose, which make this book quite unique. The key novelty and unique feature of the book is that, in this first part, analogous topics on different algebraic structures are considered simultaneously for example, the section on substructures introduces subgroups, subrings, subfields, etc.
This organization of the book is coherent and surprisingly efficient; it certainly provides a serious alternative to the traditional one where groups, rings, and fields are treated independently.
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It is interesting to compare the chapters by their styles; for instance, in Chapter 1, the reader can see only some simple examples that may already be familiar, but Chapter 2 consists completely of examples. Ultimately, the main purpose of Part 1 is to provide some basic language of algebraic structures in order to create necessary machinery for Part 2.
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