Let R and S be PIDs, and assume that R is a subring of S. Assume the following about R and S: If,...

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Let R and S be PIDs, and assume that R is a subring of S.

Assume the following about R and S: If, for an element $sES$ , there exists a non-zero $TER$ with $rs \epsilon R$ , then $s \epsilon R$ . Show: If $dER$ is a greatest common divisor in S for two elements a and b in R (not both 0), then d is a greatest common divisor for a and b in R.

sES
TER

dER

math Advanced-Math

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Answer #1

et Rand S a 1 and-Res 10 Subro 2 3ES and 3 a than ER oER (not both gaso- then E R i n

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