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April 30th, 2008, 02:04 AM   #1
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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 !
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April 30th, 2008, 05:27 AM   #2
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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.
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May 2nd, 2008, 04:20 AM   #3
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Thank you very much for your help !

I also think now there is no name for that structure.
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August 13th, 2008, 02:16 PM   #4
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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.
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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").
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August 14th, 2008, 12:04 PM   #6
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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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