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Description
Elements of Abstract AlgebraThis concise, readable, college level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems. Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as
This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory) reviews linear algebra and introduces fields as a prelude to Galois theory. In addition there is a full discussion of the constructibility of regular polygons. Chapter IV (Galois Theory) gives a thorough treatment of this classical topic, including a detailed presentation of the solvability of equations in radicals that actually includes solutions of equations of degree 3 and 4 ― a feature omitted from all texts of the last 40 years. Chapter V (Ring Theory) contains basic information about rings and unique factorization to set the stage for classical ideal theory. Chapter VI (Classical Ideal Theory) ends with an elementary proof of the Fundamental Theorem of Algebraic Number Theory for the special case of Galois extensions of the rational field, a result which brings together all the major themes of the book.
The writing is clear and careful throughout, and includes many historical notes. Mathematical proof is emphasized. The text comprises 198 articles ranging in length from a paragraph to a page or two, pitched at a level that encourages careful reading. Most articles are accompanied by exercises, varying in level from the simple to the difficult.
Binding Type: Paperback
Publisher: Dover Publications
Published: 10/01/1984
ISBN: 9780486647258
Pages: 224
Weight: 0.60lbs
Size: 8.40h x 5.50w x 0.50d
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4.5 ★★★★★
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★★★★★ 5
Don't Settle For Less
Format: Paperback
This book gave me the revelation and encouragement to get back what the enemy had stolen. Persistence is a key. This book increased my faith to receive God's promises for our lives. I learned to not be weary in well doing. My wife and I received much breakthrough. I sometimes revisit this book for a fresh reminder. This book is full of revelation and encouragement. It isn't just information but teaches you to put into practice a path to being an overcomer.
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Reviewed in the United States on March 27, 2026
★★★★★ 5
Wonderful
Format: Paperback
Wonderful book! Jane does such a great job of digging deep into scripture and yet making it accessible.
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Reviewed in the United States on April 5, 2026
★★★★★ 5
Recovery for Physical & Spiritual Losses!
Format: Paperback, Format: Paperback
9/22/24:God's timing is perfect, as is the timing of the release of this book, as I'm walking through an extended loss period and am ready to move on to the next chapter of my life (nicknamed "Job"). I first learned about this book via an author interview on CBN's "700 Club;" which totally piqued my interest, so I ordered it. Honestly, it was difficult for me to get through the forward & intro; however, I feel like the spirit of "distraction" was fighting me, warring against me taking back what I've lost via God. I powered through (while receiving an amazing amount of info from author), and by the time I got through the first several pages of chapter 1, the author's writing style relaxed, information flow slowed (going from drinking out of a fire hydrant to sipping out of a hose), it's become an easier read, full of great detailed information, scriptures for validation, deeply meaningful prayers & contracts offered as instruments for your recovery- use as weapons & armor against the enemy (if you choose), as well as examples of real life applications & their baffling/astounding results (as a visual learner this helped me visualize how these methods can be applied & worked). Jane Hamon writes this book in a way that you can IMMEDIATELY apply what you've read to your life- no need to wait to the end & tie it up all together with a neat bow. I will be able to apply this to many areas of my life & lives of others. Jane also included several pages of "Notes," enabling you to dig deeper into the various subjects & info the author reviewed for this amazing book.
I've already sent this to people I know are suffering & open to hearing this word & immediately apply these prayers, contracts, exercises, etc to their lives. Remember, this IS a WAR FOR YOUR SOUL! Don't let distractions/evil pull you away from working through this towards your victory! I pray you are successful in heavenly replevin recovery, standing in the light of God, with the Holy Spirit riding within your heart, and Christ as your lamp that lights your path. God bless you.
THANK YOU JANE HAMON!
9/24/24: To correct MISINFORMATION IN OTHER REVIEWS: In first 2 chapters alone, these Bible versions are specifically quoted:
TPT, NIV, NLT, NASB, KJV, ESV, MSG... possibly more, but I just skimmed to bring forward this CORRECT info.
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Reviewed in the United States on September 22, 2024
★★★★★ 5
Excellent Read with Awesome Declarations and Decrees
Format: Paperback
This is a really good book. I heard about the author on ElijahStreams. She is not only a good author and know what she is talking about, she is also a good preacher/teacher. I recommend this book. Use the decrees and declare them OUT LOUD!
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Reviewed in the United States on December 13, 2025
★★★★★ 5
Very good
Format: Audiobook
Great book I recommend
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Reviewed in the United States on January 30, 2026