Re: signed zero and unary minus?

>Every group that has an identity
>element and, if for each element of the group there is a unique
>element such that the group's operator applied to those elements
>yields the identity, the inverse operation is well defined.

Perhaps it has been too long since I took group theory, but IIRC a group
MUST have an identity element or two, it can have a separate left-identity
and right-identity, which may not always (?) be the same, but without one
(or two) identity elements it doesn't make it as a group.

Now, if you are talking about a SECOND operation, like multiplication for
integers, instead of addition, then there is no requirement for inverses or
identity relative to the second operation unless you want to impose even more
structure and require a division ring or a field.

Dang, I'm going to have to dig out the Herstein and refresh myself on this.
.