So, according to definitions given in https://en.wikipedia.org/wiki/Principal_ideal left principal ideal is $\{ra:r\in R\}$, right principal ideal is $\{ar:r\in R\}$. Now, i was curious what the two sided ideal actually is, because the $\{r_1as_1+\ldots+r_nas_n:r_1,s_1,\ldots,r_n,s_n\in R\}$ really contrast with the two. The explanation is given that it is to ensure that the ideal (e.g. the subring) is closed under addition, now, what is the $n$ in the sum? Does that denote finite amount of elements in $R$ or if $R$ is infinite, then we simply take the double sum $\sum_i\sum_jr_ias_j$, or how should I actually grasp this? Thanks for explanation.
2026-03-27 10:09:42.1774606182
Question regarding the definition of principal ideal
31 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in RING-THEORY
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