Not quite a ring...
- From: "Felicis" <Felicis@xxxxxxxxx>
- Date: Wed, 28 Feb 2007 14:30:07 +0000 (UTC)
If we take a set S and two binary operations, + and * so that <S,+,*>
is a ring, then <S,+> is an abelian group.
But- what if we don't want to limit <S,+> quite so much? I understand
*why* we want <S,+> to be an abelian group - and I have found that if
we allow <S,+> to be a group and limit the distributive property to
just left-distribution, then we get a near-ring. But I noticed that
*:SxS --> S does not have to be onto. So another solution could be to
have <S,+> be a group (possibly non-abelian), and have * defined to
map SxS onto Z(<S,+>), (Where Z(<S,+>) is the center of <S,+>) and
keeping both left and right distribution in place. I have been
calling such a structure a 'pseudo-ring', but am wondering if anyone
else has looked at structures like this, and if so to what use they
might be put (or if there are any natural examples that come up)? And
what resources I might look for to examine this more fully?
Thank you-
Eric Riley
.
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