Let R be a finite commutative ring, that is if a, b are elements of R, then ab = ba.

Show that for any t R, T = tR = {tr|r R} is a subring of R

Further, if T R, there are r1 r2 such that tr1 = tr2. (Hint: if tr ts for all r, s R,

then #tR = #R. )

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- Feb 19th 2013, 06:52 PMjll90Abstract Algebra - Rings and Subrings
Let R be a finite commutative ring, that is if a, b are elements of R, then ab = ba.

Show that for any t R, T = tR = {tr|r R} is a subring of R

Further, if T R, there are r1 r2 such that tr1 = tr2. (Hint: if tr ts for all r, s R,

then #tR = #R. ) - Feb 19th 2013, 07:28 PMjakncokeRe: Abstract Algebra - Rings and Subrings
Closed under multiplication? , so closed under multi.

Closed under subtraction? , so closed under subtraction

The third thing. If T = R, then they would have to be the same "size" no? meaning if and then what were originally 2 elements in R collapsed into one element in T (thus making it smaller and thus not equal to R).