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MHB What distinguishes a Field from a Ring?

Thread starter highmath
Start date Dec 19, 2018
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Field Ring

Dec 19, 2018

#1

highmath

What the differences between Field and Ring?

Physics news on Phys.org

Dec 19, 2018

#2

Ackbach

Gold Member

MHB

A ring isn't necessarily commutative in its multiplication, and doesn't necessarily have multiplicative inverses. Some authors assume rings have a multiplicative identity $1$, other authors don't. Addition is the same.

Thread 'About the existence of Hamel basis for vector spaces'

It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC). Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?

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