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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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4.2 ★★★★★
Based on 6 reviews
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Product Reviews
★★★★★ 5
Great toy for dogs
Color: Red
My dog loves this toy, it was well worth the money. And I’m glad it charges with USB and not batteries.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on June 8, 2026
★★★★★ 4
Finally, a Toy That Out-Works My Dog!
Color: Blue
My dog gets bored easily, and this automatic moving ball has been a hilarious and effective distraction. It bounces and rotates on its own, which triggers her hunting instinct immediately. The rope chew attached to the side is a nice touch for some added teeth cleaning while she plays. It’s sturdy enough for a medium-sized dog and the fact that it's waterproof means I don't have to worry when she eventually drops it in the water bowl or takes it out into the melting snow. The *only* issue I have is it starts before I can even screw it back together. It wants to jump out of my hands before I'm ready.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on February 19, 2026
★★★★★ 5
My dogs think this is either terrifying or amazing
Color: Blue
I got this interactive dog toy thinking it would turn my living room into a fun little chase arena for my two small dogs. Technically, it did create excitement, but not in the way I expected. The toy rolls around unpredictably and wiggles its rope like it is trying to escape, which is honestly hilarious to watch. The movement is surprisingly energetic and the different speed modes keep it from feeling repetitive or robotic. The battery life is decent and it charges quickly, so it is easy to keep it ready for playtime.
Now for the comedy... my one year old Silky Terrier is normally the fearless one. He charges vacuum cleaners, interrogates delivery boxes, and believes he is the head of household security. However, the moment this toy turns on and starts moving, he suddenly remembers he has very important business somewhere else. He will sit at a safe distance and stare at it like it might file a police report against him.
The funny part is that when the toy is turned off, it instantly becomes his favorite object in the house. He happily grabs the rope, drags it around, chews on it, and proudly carries it like a trophy. Apparently his bravery only applies when the toy is not alive. I have discovered that in my house this is considered the acceptable mode of operation.
My seven year old Yorkie is even wiser. She took one look at the moving toy, processed the situation for approximately three seconds, and decided she would absolutely not be participating in whatever nonsense was happening on the floor. She calmly walked away and has maintained that policy ever since. She clearly understands this toy and wants no part of it.
Overall the toy is well made, entertaining, and definitely capable of keeping energetic dogs busy. Even if your dogs end up like mine and treat it as either a suspicious creature or a decorative rope toy, it still provides plenty of entertainment for the humans watching the situation unfold. If your dog enjoys chasing unpredictable moving toys, this one will probably become a household favorite. If not, you may at least get a very funny show out of it. 🐶
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Reviewed in the United States on March 10, 2026
★★★★★ 3
Just another reason to bark.
Color: Blue
I was so excited to come across this Interactive Dog Toy from Mewzoo, figuring that it would be a great way to give our dog some inside exercise during the rainy season that we have in this neck of the woods. It arrives with a charger, instructions and two ropes that can be tied to it, and it took about 2 hours to get it fully charged.
In order to get it moving, one needs to unscrew the blue plastic piece and that gives access to the control inside of it. It has three speeds, but the faster speeds only seem to lessen the time intervals for when it moves, they don't make it move any faster or further. This is kind of a bummer, because it really does not move very far, it mostly just stays within a foot or two of where it started. So not much exercise potential here, unless you consider barking exercise. Barking is one thing we do not need more of in this household, so this toy is a bit of a flop for us. I imagined that our boy might run circles around it and get a bit more hyper, maybe even grab it by the rope and carry it around for a bit. In the beginning I think he was fearful because he just barked at it of it, and then he decided it was time to eat. As you can see in the video, after only a few minutes with it, it looks like he's decided it's just a nuisance, lol.
The concept is good, and the toy itself is reasonably constructed to withstand some playtime. I just think it needs to have more movement and skitter around better to cover more distance. Then again at the whopping price of $10.99, i really can't complain.
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Reviewed in the United States on February 21, 2026
★★★★★ 1
My dog was scared
Color: Blue
It scared my dog, he didn’t like it at all.
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Reviewed in the United States on June 8, 2026
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