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Description
Lattice Theory: First Concepts and Distributive LatticesLattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end of chapter materials and references. Both novices and experts will benefit from this
Lattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references.Both novices and experts will benefit from this treatment, which combines the techniques of an introductory text with those of a monograph. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices. Diagrams constitute an integral part of the book, along with 500 exercises and 67 original research problems. Eight appendixes, contributed by a group of experts, complement this accessible and informative text.
Binding Type: Paperback
Publisher: Dover Publications
Published: 03/26/2009
ISBN: 9780486471730
Pages: 212
Weight: 0.45lbs
Size: 8.10h x 5.20w x 0.60d
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4.6 ★★★★★
Based on 8 reviews
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Product Reviews
★★★★★ 1
Dog ends up eating plastic ends
Size: For Medium Dog, Color: Grassgreen
At first I thought this would be a great toy but in reality the design doesn’t make sense. The little pieces ‘pricks’ of the cactus get chewed off and swallowed by the dog. So you’re essentially feeding them plastic.
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Reviewed in the United States on May 1, 2026
★★★★★ 5
AMAZING for my Doberman
Size: For Medium Dog, Color: Grassgreen, Size: For Medium Dog, Color: Grassgreen
This toy is the absolute BEST! It has out lasted every other toy by a long shot. So far it has lasted 7 months with a very tough chewer. No other toy has lasted more than a week or two aside from this one. I got this the same week I got my Doberman puppy. I am very impressed how well it has lasted so far. It’s still in great shape but is missing some of the “spikes” and has some tooth indents. Squeezer still works well too. It’s one of his favorite toys.
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Reviewed in the United States on December 1, 2025
★★★★★ 5
Puppy loves it! Great activity.
Size: For Medium Dog, Color: Grassgreen
My 5 month old puppy absolutely loves this toy. She spends hours chewing on it and squeaking. It’s heavy enough duty that she can’t bite the side parts off but she can munch on it at the back of her teeth. Great for cleaning teeth! She did bite some of the little nubs off but I expected some of that. It’s really the perfect hardness for her. Worth buying!
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Reviewed in the United States on April 30, 2026
★★★★★ 5
Incredibly durable
Size: For Medium Dog, Color: Grassgreen, Size: For Medium Dog, Color: Grassgreen
I bought this for my malinois mix when i got her last august. She's 10 months old and plays with this toy every day. This is such a durable toy! I strongly suggest this for everyone
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Reviewed in the United States on May 3, 2026
★★★★★ 4
He loves it! It will probably be destroyed soon though...
Size: For Medium Dog, Color: Green, Size: For Medium Dog, Color: Green
Update! This toy has definitely withstood my boy's daily chewing! It's lost some pieces for sure, but overall it's holding up and I'm very happy about it. The only downside is the squeaker is rather difficult to get to make noise. Will still definitely invest in another when this one finally goes.
Original review: I bought this for my handsome pitbull/boxer mix -- the boy loves to chew toys up! He's an aggressive chewer and he was bored with the current toys we had.
This toy is advertised for chewers, and I imagine if my boy wasn't such a great chewer, it would be amazing! We've had it three days now and he's already gotten a few big chunks off of it. It is definitely entertaining him though! He loves it and he seems like he's chewed himself into a daze. There is a squeaker in the bottom that seems difficult for him to get to so it doesn't squeak often -- when it does though he freaks and it's hilarious.
Overall I'm very happy with this purchase. My boy is a very aggressive chewer and I know pretty much anything we get him will be destroyed soon after he gets it. With how much he is enjoying this toy, I will be buying it again for him.
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Reviewed in the United States on November 18, 2023