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   The Axioms of Algebraic Structures
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   Author  Topic: The Axioms of Algebraic Structures  (Read 5399 times)
peoplepower
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The Axioms of Algebraic Structures  
« on: Oct 30th, 2012, 3:26pm »
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Here are three problems. Two of which I know for a fact are well known, and the other I can only assume is well known.
 
Easiest: Let R be a ring (with identity) possibly with noncommutative addition. Prove that addition commutes anyway.
Easy: Let G be a finite set equipped with an operation (juxtaposition) such that left cancellation and right cancellation both hold. Prove that G is a group.
Easy-Medium: Let G be a set equipped with an operation (juxtaposition) such that there is a left identity and for every element there is a left inverse. Prove that G is a group.
« Last Edit: Oct 30th, 2012, 3:32pm by peoplepower » IP Logged
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