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wu :: forums    riddles    putnam exam (pure math) (Moderators: Grimbal, william wu, Icarus, Eigenray, towr, SMQ)    The Axioms of Algebraic Structures « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: The Axioms of Algebraic Structures  (Read 5436 times) peoplepower Junior Member     Posts: 63 The Axioms of Algebraic Structures   « on: Oct 30th, 2012, 3:26pm » Quote Modify 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 Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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