Re: What is the name of this RING

On Jun 15, 6:45 pm, fjbl...@xxxxxxxxx wrote:
On Jun 15, 11:35 am, plx...@xxxxxxxxx wrote:

Dear abstract algebra experts -

I do not even know enough to do a search for this answer!

What is the name of the ring consisting of the four matrices:

1 0 0 1 -1 0 0 1
0 1 1 0 0 1 -1 0

like SO(2) or some *** like that

It's not a ring, because it isn't closed under addition.

Those four matrices form a *group* under matrix multiplication, which
is isomorphic to K_4 = Z_2 x Z_2, the so called Klein group.

Is that it, or did you mean something else?

The third matrix times the second matrix is

0 -1
1 0

which is not on the list. However, I think the group closes if you
include the additive inverses of each matrix.

--
Jim E. Black

.

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