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 April 30th, 2008, 02:04 AM #1 Newbie   Joined: Apr 2008 Posts: 2 Thanks: 0 Ring and pseudo-ring Hello everybody, A ring where the identity element does not exists is called a pseudo-ring. 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 "pseudo-ring" came up with a different entity. It looks like that sense of pseudo-ring 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 pseudo-ring 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 "near-ring", in which multiplication is only right-distributive over addition. As for a structure that does not call for distributivity, I don't know.
August 14th, 2008, 04:30 AM   #5
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Re: Ring and pseudo-ring

Quote:
 Originally Posted by Spartan Math Actually...I believe it's called a "rung", or at least my book "An Introduction to Ring Theory" calls it.
You mean a ring without identity? I've seen "ring" (for which the standard is called "ring with identity") as well as "rng" (cute, "ring" without the "i").

 August 14th, 2008, 12:04 PM #6 Member   Joined: Aug 2008 Posts: 84 Thanks: 0 Re: Ring and pseudo-ring 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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