Let a belong to a ring R. Let S={x in R | ax=0} . Show that S is a subring of R.

Maiclubk 2021-02-11 Answered
Let a belong to a ring R. Let S={xRax=0} . Show that S is a subring of R.
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au4gsf
Answered 2021-02-12 Author has 95 answers

To show a non-empty subset S of R is a subring if a,bSabSandabS
Clearly S is non-empty as 0 belongs to Ring R so, ax=0.
let x,yS ax=0,ay=0
is is needed to show that xyS
consider, axay=a(xy)S
as xyR
Now show xyS
consider, (ax)(ay)=00=0
a2(xy)=b(xy)=0[a=bxyR]
thus, xyS
Therefore, S is a subring of ring R.

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