Let R = K [ x , y , z ] / ( x 3 + y 3 + z 3 ) {\displaystyle {}R=K[x,y,z]/{\left(x^{3}+y^{3}+z^{3}\right)}} , where K {\displaystyle {}K} is a field of positive characteristic p ≠ 3 {\displaystyle {}p\neq 3} , I = ( x 2 , y 2 , z 2 ) {\displaystyle {}I={\left(x^{2},y^{2},z^{2}\right)}} , and
The equation x 3 + y 3 + z 3 = 0 {\displaystyle {}x^{3}+y^{3}+z^{3}=0} yields the short exact sequence
This shows that Syz ( x 2 , y 2 , z 2 ) {\displaystyle {}\operatorname {Syz} {\left(x^{2},y^{2},z^{2}\right)}} is strongly semistable.
![{\displaystyle {}R=K[x,y,z]/{\left(x^{3}+y^{3}+z^{3}\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2722b02c356e14da5c016d2297849e225564039)
,
where 
is a field of positive characteristic
,
,
and
yields the short exact sequence
is strongly semistable.
