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Diberikan sebarang ring $R$ dan $R$ . Dibentak himpunan $aR= \{ar|r \in R\}$ dan $Ra= \{ra|r \in R\}$

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Csc, sec, and cot of special angles

Full solution

Q. Diberikan sebarang ring

R

dan

R

. Dibentak himpunan

aR= \{ar|r \in R\}

dan

Ra= \{ra|r \in R\}

Understand Definitions: To solve this problem, we need to understand the definition of the sets $aR$ and $Ra$ in the context of ring theory. In ring theory, if $R$ is a ring and $a$ is an element of $R$ , then the set $aR$ is defined as the set of all products of $a$ with elements of $R$ . Similarly, $Ra$ is the set of all products of elements of $R$ with $a$ . Let's write down these definitions formally.
Define set $aR$ : Now, let's define the set $aR$ . For any element $r$ in $R$ , the product $ar$ is in $aR$ . Therefore, $aR = \{ar | r \in R\}$ . This means $aR$ is the set of all elements that can be formed by multiplying $a$ with every element $r$ in the ring $R$ .
Define set $R_a$ : Next, we define the set $R_a$ . For any element $r$ in $R$ , the product $ra$ is in $R_a$ . Therefore, $R_a = \{ra | r \in R\}$ . This means $R_a$ is the set of all elements that can be formed by multiplying every element $r$ in the ring $R$ with $R_a$ $0$ .

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