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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 ★★★★★
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Product Reviews
★★★★★ 5
Worked for Volvo Penta SX Gimbal Bearing
Very heavy tool, I was surprised. Pulled my bearing like it was nothing. Putting the new bearing in was a little more difficult as you have to drill a hole in the engine alignment shaft where it will work for your particular outdrive. Not hard, but it does not come pre-drilled as the required depth for each particular gimbal bearing differs by manufacturer and model. Measure your bearing placement before removal and check that it was installed correctly in the first place. The bearing should line up with the grease fitting and the o-rings on the drive shaft should end up riding in the middle of the bearing. once you have your measurement drill the hole, I used a drill press. I suppose you could use it on multiple outdrive models as long as you can drill more holes.
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Reviewed in the United States on June 5, 2023
★★★★★ 5
Great value
This kit worked perfectly on my Alpha one mercury outdrive. I saw a lot of people mention that it was a hassle to drill the hole when you better have all this alignment stuff. I threw it in use my regular drill drill guide and then the second hole was lined up. Pulling Gimble be very easy. I did have to adjust it up at an angle because my bearing was sitting in their crooked and it came out the second time I made the adjustment to the angle. I would highly recommend this.
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Reviewed in the United States on April 16, 2024
★★★★★ 1
Unfinished product - doesn't work - waste of money
in order to use this as an installation tool the directions tell you to drill a hole through the 2 inch steel rod..... either this hole should already be drilled, or this should not be advertised as an installation tool..... it will not install any bearings without extensive modification and requires the use of a drill press or a lathe. very dissatisfied that I now have to buy ANOTHER tool just to finish this job because this one doesn't do what it's described to do.... piece of junk... typical amazon garbage.... this is why I haven't used amazon in over a year... they rip you off with garbage.... I should have known better .... don't buy this junk .... Now they say 20 -30 days to get my refund .... Don't waste your time
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Reviewed in the United States on May 26, 2026
★★★★★ 5
Good tool, but must be hand drilled to accept bearing installation cup
Good tool, but you have to drill a hole in the bearing installation rod to accept the cross bolt that locks the bearing installation cup onto the rod.
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Reviewed in the United States on January 23, 2023
★★★★★ 5
Worked well
Worked well
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Reviewed in the United States on October 31, 2025