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April 30th, 2008, 02:04 AM  #1 
Newbie Joined: Apr 2008 Posts: 2 Thanks: 0  Ring and pseudoring
Hello everybody, A ring where the identity element does not exists is called a pseudoring. Is there a name for a ring where multiplication is not distributive over addition ? Thank you for your help ! 
April 30th, 2008, 05:27 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I don't think there's any terminology for either a ring without an identity or a ring that does not distribute. My searches for "pseudoring" came up with a different entity. It looks like that sense of pseudoring is one of Bourbaki's. 
May 2nd, 2008, 04:20 AM  #3 
Newbie Joined: Apr 2008 Posts: 2 Thanks: 0 
Thank you very much for your help ! I also think now there is no name for that structure. 
August 13th, 2008, 02:16 PM  #4 
Member Joined: Aug 2008 Posts: 84 Thanks: 0  Re: Ring and pseudoring
Actually...I believe it's called a "rung", or at least my book "An Introduction to Ring Theory" calls it. As for the second structure, there is such a thing as a "nearring", in which multiplication is only rightdistributive over addition. As for a structure that does not call for distributivity, I don't know.

August 14th, 2008, 04:30 AM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Ring and pseudoring Quote:
 
August 14th, 2008, 12:04 PM  #6 
Member Joined: Aug 2008 Posts: 84 Thanks: 0  Re: Ring and pseudoring
well, on Wikipedia I've seen "Rng" but in my book I saw "Rung", though I suspect "Rng" is the more mainstream term.


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