My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 28th, 2014, 11:23 AM   #1
Newbie
 
MathMadness's Avatar
 
Joined: May 2014
From: Brandon, MS

Posts: 2
Thanks: 0

Question Factorial Domain

I need to find a factorial domain which does not contain a field.

I know a factorial domain is an integral domain where every non-unit has a unique factorization.

I know an integral domain is a ring whose non-zero elements are non-zero divisors.

Help!
MathMadness is offline  
 
May 28th, 2014, 12:11 PM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
What does it mean to contain a field? Surely the set containing only 0 and 1 is a subring and this ring is itself a field. (All domains contain distinct elements 0 and 1.)
CRGreathouse is offline  
May 28th, 2014, 01:28 PM   #3
Senior Member
 
Joined: Nov 2010
From: Berkeley, CA

Posts: 174
Thanks: 35

Math Focus: Elementary Number Theory, Algebraic NT, Analytic NT
But 1+1 is not necessarily equal to 0, so {0,1} may not be closed under addition.
Petek is offline  
May 28th, 2014, 02:13 PM   #4
Senior Member
 
Joined: Mar 2012

Posts: 294
Thanks: 88

Hint: there is an obvious one you have known since childhood.
Deveno is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
domain, factorial, field



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
factorial rakmo Algebra 5 June 16th, 2013 09:13 AM
cos with factorial. ZardoZ Real Analysis 15 April 17th, 2013 12:47 AM
n! (factorial) thomasthomas Number Theory 13 November 6th, 2010 06:21 AM
Integration over open domain or close domain good_phy Calculus 1 October 12th, 2008 09:26 AM
zero factorial (why ??) sangfroid Number Theory 8 September 15th, 2008 04:28 AM





Copyright © 2019 My Math Forum. All rights reserved.