New to the board and neep help:
Find the units of the ring R when R is
(i) Z x Z
(ii) F(e), where F is a field and e^2=0.
(iii) M2(F), where F is a field and M2 is a two-by-two matrix.
Thank you.
The units in $\displaystyle \mathbb{Z}$ are $\displaystyle -1,1$
Thus,
$\displaystyle (-1,1),(-1,-1),(1,-1),(1,1)$
This is called a trivial ring, or the ring where $\displaystyle 1=0$(ii) F(e), where F is a field and e^2=0.
The additive element is the only unit.
Unless the notion F(e) means something else?
(It cannot possibly means a simple extension).
All invertible matrices, that is,(iii) M2(F), where F is a field and M2 is a two-by-two matrix.
$\displaystyle \det (A)\not = 0$