# condition on a near ring to be a ring

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Type of Math Object:
Theorem
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Reference
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## Mathematics Subject Classification

The terms "additive identity" and "additive inverse" currently do not link properly. This should be fixed, and there are several ways that this can be accomplished:

1. Declare that some entry defines these terms and file an addendum to that entry if necessary. The candidates are "ring" and "near ring".

2. Declare that "uniqueness of additive identity in a ring" and "uniqueness of additive inverse in a ring" define these terms respectively and file addenda to these entries if necessary. (In light of the fact that an additive identity and additive inverses exist in near rings, perhaps these two entries can be generalized.)

3. Define these terms in a separate entry (either together or one for each).

Or maybe there is an even better option that has not come to my mind.

Any thoughts?

Warren

I like the first option, since an additive identity and an additive inverse of an element are defined without requiring that they be unique.

Better yet, you can define left and right (additive) identities and inverses. In this more general setting, you may end up with multiple identities and inverses.

> Better yet, you can define left and right (additive) identities and inverses. In this more general setting, you may end up with multiple identities and inverses.

Good point. A set does not need to be a ring (or even a near ring) to have an addition operation defined on it. On the other hand, I am unsure about applications of having a noncommutative addition operation, especially if the set also has a multiplication operation defined on it. Do people study such sets?