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chwala
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- Am just but refreshing (kindly see highlihted part)
...this element ##r## can only be ##0## correct? The zero ring has only one element which is ##0##.
The zero element in a ring is used to represent the additive identity, meaning that when it is added to any other element in the ring, it does not change the value of that element.
The zero element is denoted by the number 0 or the symbol ∅ in a ring.
No, there can only be one zero element in a ring. This is because the zero element must satisfy certain properties, such as being the additive identity, and having more than one zero element would violate these properties.
When the zero element is multiplied by any other element in a ring, the result is always the zero element. This is because the zero element acts as an absorbing element for multiplication.
No, the concept of a zero element exists in other algebraic structures as well, such as groups and fields. However, the properties and behavior of the zero element may differ slightly in these structures.